JEE Main & Advanced Mathematics Linear Programming Question Bank

done Linear Programming Total Questions - 75

• question_answer1)
  For the constraint of a linear optimizing function \[z={{x}_{1}}+{{x}_{2}}\], given  by \[{{x}_{1}}+{{x}_{2}}\le 1,\ 3{{x}_{1}}+{{x}_{2}}\ge 3\] and \[{{x}_{1}},\ {{x}_{2}}\ge 0\]
  A)
                  There are two feasible regions done clear
  B)
                  There are infinite feasible regions done clear
  C)
                  There is no feasible region           done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer2)
  Which of the following is not a vertex of the positive region bounded by the inequalities \[2x+3y\le 6\], \[5x+3y\le 15\] and \[x,\ y\ge 0\]
  A)
                  (0, 2)      done clear
  B)
                  (0, 0) done clear
  C)
                  (3, 0)      done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer3)
  The intermediate solutions of constraints must be checked by substituting them back into 
  A)
                  Objective function          done clear
  B)
                  Constraint equations done clear
  C)
                  Not required      done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer4)
  For the constraints of a L.P. problem given by \[{{x}_{1}}+2{{x}_{2}}\le 2000\],\[{{x}_{1}}+{{x}_{2}}\le 1500\],\[{{x}_{2}}\le 600\]and \[{{x}_{1}},\ {{x}_{2}}\ge 0\], which one of the following points does not lie in the positive bounded region 
  A)
                  (1000, 0)               done clear
  B)
                  (0, 500) done clear
  C)
                  (2, 0)      done clear
  D)
                  (2000, 0) done clear
  View Solution play_arrow

• question_answer5)
  A basic solution is called non-degenerate, if 
  A)
                  All the basic variables are zero   done clear
  B)
                  None of the basic variables is zero done clear
  C)
                  At least one of the basic variables is zero done clear
  D)
                  None of these done clear
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• question_answer6)
  If the number of available constraints is 3 and the number of parameters to be optimized is 4, then 
  A)
                  The objective function can be optimized done clear
  B)
                  The constraints are short in number done clear
  C)
                  The solution is problem oriented done clear
  D)
                  None of these done clear
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• question_answer7)
  The solution of set of constraints \[x+2y\ge 11,\] \[3x+4y\le 30,\ \ 2x+5y\le 30,\ x\ge 0,\ \ y\ge 0\] includes the point  [MP PET 1993]
  A)
                  (2, 3)      done clear
  B)
                  (3, 2) done clear
  C)
                  (3, 4)      done clear
  D)
                  (4, 3) done clear
  View Solution play_arrow

• question_answer8)
  The graph of \[x\le 2\] and \[y\ge 2\] will be situated in the 
  A)
                  First and second quadrant           done clear
  B)
                  Second and third quadrant done clear
  C)
                  First and third quadrant done clear
  D)
                  Third and fourth quadrant done clear
  View Solution play_arrow

• question_answer9)
  The feasible solution of a L.P.P. belongs to 
  A)
                  First and second quadrant           done clear
  B)
                  First and third quadrant done clear
  C)
                  Second quadrant             done clear
  D)
                  Only first quadrant done clear
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• question_answer10)
  The position of points O (0,0) and P (2, ? 2) in the region of graph of inequation \[2x-3y<5\], will be  
  A)
                  O inside and P outside   done clear
  B)
                  O and P both inside done clear
  C)
                  O and P both outside done clear
  D)
                  O outside and P inside done clear
  View Solution play_arrow

• question_answer11)
  The true statement for the graph of inequations \[3x+2y\le 6\] and \[6x+4y\ge 20\], is  
  A)
                  Both graphs are disjoint                done clear
  B)
                  Both do not contain origin done clear
  C)
                  Both contain point (1, 1)               done clear
  D)
                  None of these done clear
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• question_answer12)
  The vertex of common graph of inequalities \[2x+y\ge 2\] and \[x-y\le 3\], is 
  A)
                  (0, 0)      done clear
  B)
                  \[\left( \frac{5}{3},\ -\frac{4}{3} \right)\] done clear
  C)
                  \[\left( \frac{5}{3},\ \frac{4}{3} \right)\] done clear
  D)
                  \[\left( -\frac{4}{3},\ \frac{5}{3} \right)\] done clear
  View Solution play_arrow

• question_answer13)
  A vertex of  bounded region of inequalities \[x\ge 0\], \[x+2y\ge 0\] and \[2x+y\le 4\], is
  A)
                  (1, 1)      done clear
  B)
                  (0, 1) done clear
  C)
                  (3, 0)      done clear
  D)
                  (0, 0) done clear
  View Solution play_arrow

• question_answer14)
  A vertex of the linear inequalities \[2x+3y\le 6\], \[x+4y\le 4\] and \[x,\ y\ge 0\], is 
  A)
                  (1, 0)      done clear
  B)
                  (1, 1) done clear
  C)
                  \[\left( \frac{12}{5},\ \frac{2}{5} \right)\]              done clear
  D)
                  \[\left( \frac{2}{5},\ \frac{12}{5} \right)\] done clear
  View Solution play_arrow

• question_answer15)
  A vertex of a feasible region by the linear constraints \[3x+4y\le 18,\ 2x+3y\ge 3\] and \[x,\ y\ge 0\], is 
  A)
                  (0, 2)      done clear
  B)
                  (4.8, 0) done clear
  C)
                  (0, 3)      done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer16)
  In which quadrant, the bounded region for inequations \[x+y\le 1\] and \[x-y\le 1\] is situated  
  A)
                  I, II          done clear
  B)
                  I, III done clear
  C)
                  II, III done clear
  D)
                  All the four quadrants done clear
  View Solution play_arrow

• question_answer17)
  The necessary condition for third quadrant region in                   xy-plane, is
  A)
                  \[x>0,\ y<0\]      done clear
  B)
                  \[x<0,\ y<0\] done clear
  C)
                  \[x<0,\ y>0\]      done clear
  D)
                  \[x<0,\ y=0\] done clear
  View Solution play_arrow

• question_answer18)
  For the following feasible region, the linear constraints are 
  A)
                  \[x\ge 0,\ y\ge 0,\ 3x+2y\ge 12,\ x+3y\ge 11\] done clear
  B)
                  \[x\ge 0,\ y\ge 0,\ 3x+2y\le 12,\ x+3y\ge 11\] done clear
  C)
                  \[x\ge 0,\ y\ge 0,\ 3x+2y\le 12,\ x+3y\le 11\] done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer19)
  The value of objective function is maximum under linear constraints 
  A)
                  At the center of feasible region done clear
  B)
                  At (0, 0) done clear
  C)
                  At any vertex of feasible region done clear
  D)
                  The vertex which is at maximum distance from (0, 0) done clear
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• question_answer20)
  The region represented by \[2x+3y-5\le 0\] and \[4x-3y+2\le 0\], is 
  A)
                  Not in first quadrant       done clear
  B)
                  Bounded in first quadrant done clear
  C)
                  Unbounded in first quadrant      done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer21)
  The region represented by the inequation system \[x,\ y\ge 0\], \[y\le 6,\ x+y\le 3\], is 
  A)
                  Unbounded in first quadrant      done clear
  B)
                  Unbounded in first and second quadrants done clear
  C)
                  Bounded in first quadrant            done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer22)
   The solution set of the inequation \[2x+y>5\], is 
  A)
                  Half plane that contains the origin done clear
  B)
                  Open half plane not containing the origin done clear
  C)
                  Whole xy-plane except the points lying on the line \[2x+y=5\]   done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer23)
  If a point (h, k) satisfies an inequation \[ax+by\ge 4\], then the half plane represented by the inequation is 
  A)
                  The half plane containing the point (h, k) but excluding the points on \[ax+by=4\]            done clear
  B)
                  The half plane containing the point (h, k) and the points on \[ax+by=4\] done clear
  C)
                  Whole xy-plane                done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer24)
  Inequation \[y-x\le 0\] represents
  A)
                  The half plane that contains the positive x-axis done clear
  B)
                  Closed half plane above the line \[y=x\] which contains positive y-axis done clear
  C)
                  Half plane that contains the negative x-axis done clear
  D)
                  None of these done clear
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• question_answer25)
  Objective function of a L.P.P. is 
  A)
                  A constraint        done clear
  B)
                  A function to be optimized done clear
  C)
                  A relation between the variables done clear
  D)
                  None of these done clear
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• question_answer26)
  The optimal value of the objective function is attained at the points         [MP PET 1998]
  A)
                  Given by intersection of inequations with axes only        done clear
  B)
                  Given by intersection of inequations with x-axis only done clear
  C)
                  Given by corner points of the feasible region done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer27)
  The objective function \[z=4x+3y\] can be maximized subjected to the constraints \[3x+4y\le 24\], \[8x+6y\le 48\], \[x\le 5,\ y\le 6;\ \ x,\ y\ge 0\]
  A)
                  At only one point             done clear
  B)
                  At two points only done clear
  C)
                  At an infinite number of points done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer28)
  If the constraints in a linear programming problem are changed
  A)
                  The problem is to be re-evaluated done clear
  B)
                  Solution is not defined done clear
  C)
                  The objective function has to be modified done clear
  D)
                  The change in constraints is ignored done clear
  View Solution play_arrow

• question_answer29)
  Which of the following statements is correct
  A)
                  Every L.P.P. admits an optimal solution done clear
  B)
                  A L.P.P. admits a unique optimal solution done clear
  C)
                  If a L.P.P. admits two optimal solutions, it has an infinite number of optimal solutions     done clear
  D)
                  The set of all feasible solutions of a L.P.P. is not a convex set done clear
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• question_answer30)
   Shaded region is represented by              [MP PET 1997]
  A)
                  \[2x+5y\ge 80,\ x+y\le 20,\ x\ge 0,\ y\le 0\]        done clear
  B)
                  \[2x+5y\ge 80,\ x+y\ge 20,\ x\ge 0,\ y\ge 0\] done clear
  C)
                  \[2x+5y\le 80,\ x+y\le 20,\ x\ge 0,\ y\ge 0\] done clear
  D)
                  \[2x+5y\le 80,\ x+y\le 20,\ x\le 0,\ y\le 0\] done clear
  View Solution play_arrow

• question_answer31)
  The constraints                       \[-{{x}_{1}}+{{x}_{2}}\le 1\]                      \[-{{x}_{1}}+3{{x}_{2}}\le 9\]                       \[{{x}_{1}},\ {{x}_{2}}\ \ge 0\] define on          [MP PET 1999]
  A)
                  Bounded feasible space                done clear
  B)
                  Unbounded feasible space done clear
  C)
                  Both bounded and unbounded feasible space   done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer32)
  Which of the following is not true for linear programming problems          [Kurukshetra CEE 1998]
  A)
                  A slack variable is a variable added to the left hand side of a less than or equal to constraint to convert it into an equality            done clear
  B)
                  A surplus variable is a variable subtracted from the left hand side of a greater than or equal to constraint to convert it into an equality done clear
  C)
                  A basic solution which is also in the feasible region is called a basic feasible solution          done clear
  D)
                  A column in the simplex tableau that contains all of the variables in the solution is called pivot or key column done clear
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• question_answer33)
  Which of the terms is not used in a linear programming problem                 [MP PET 2000]
  A)
                  Slack variables   done clear
  B)
                  Objective function done clear
  C)
                  Concave region                 done clear
  D)
                  Feasible solution done clear
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• question_answer34)
  The graph of inequations \[x\le y\] and \[y\le x+3\] is located in
  A)
                  II quadrant          done clear
  B)
                  I, II quadrants done clear
  C)
                  I, II, III quadrants              done clear
  D)
                  II, III, IV quadrants done clear
  View Solution play_arrow

• question_answer35)
  The area of the feasible region for the following constraints \[3y+x\ge 3,\,x\ge 0,\,y\ge 0\] will be           [DCE 2005]
  A)
                  Bounded             done clear
  B)
                  Unbounded done clear
  C)
                  Convex done clear
  D)
                  Concave done clear
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• question_answer36)
  The feasible region for the following constraints \[{{L}_{1}}\le 0,{{L}_{2}}\ge 0,\,{{L}_{3}}=0,\,x\ge 0,y\ge 0\] in the diagram shown is                                             [Kerala (Engg.) 2005]                                                                                                                
  A)
                  Area DHF             done clear
  B)
                  Area AHC done clear
  C)
                  Line segment EG              done clear
  D)
                  Line segment GI done clear
  E)
                  Line segment IC done clear
  View Solution play_arrow

• question_answer37)
  A wholesale merchant wants to start the business of cereal with Rs. 24000. Wheat is Rs. 400 per quintal and rice is Rs. 600 per quintal. He has capacity to store 200 quintal cereal. He earns the profit Rs. 25 per quintal on wheat and Rs. 40 per quintal on rice. If he stores x quintal rice and y quintal wheat, then for maximum profit the objective function is     
  A)
                  \[25x+40y\]        done clear
  B)
                  \[40x+25y\] done clear
  C)
                  \[400x+600y\]   done clear
  D)
                  \[\frac{400}{40}x+\frac{600}{25}y\] done clear
  View Solution play_arrow

• question_answer38)
  Mohan wants to invest the total amount of Rs. 15,000 in saving certificates and national saving bonds. According to rules, he has to invest at least Rs. 2000 in saving certificates and Rs. 2500 in national saving bonds. The interest rate is 8% on saving certificate and 10% on national saving bonds per annum. He invest Rs. x in saving certificates and Rs. y in national saving bonds. Then the objective function for this problem is 
  A)
                  \[0.08x+0.10y\] done clear
  B)
                  \[\frac{x}{2000}+\frac{y}{2500}\] done clear
  C)
                  \[2000x+2500y\]               done clear
  D)
                  \[\frac{x}{8}+\frac{y}{10}\] done clear
  View Solution play_arrow

• question_answer39)
  A firm produces two types of products A and B. The profit on both is Rs. 2 per item. Every product requires processing on machines \[{{M}_{1}}\] and \[{{M}_{2}}\]. For A, machines \[{{M}_{1}}\] and \[{{M}_{2}}\] takes 1 minute and 2 minute respectively and for B, machines \[{{M}_{1}}\] and \[{{M}_{2}}\] takes the time 1 minute each. The machines \[{{M}_{1}},\ {{M}_{2}}\] are not available more than 8 hours and 10 hours, any of day, respectively. If the products made x of A and y of B, then the linear constraints for the L.P.P. except \[x\ge 0,\ y\ge 0\], are    
  A)
                  \[x+y\le 480\,,\ 2x+y\le 600\] done clear
  B)
                  \[x+y\le 8,\ 2x+y\le 10\] done clear
  C)
                  \[x+y\ge 480\,,\ 2x+y\ge 600\] done clear
  D)
                  \[x+y\le 8,\ 2x+y\ge 10\] done clear
  View Solution play_arrow

• question_answer40)
  The objective function in the above question is
  A)
                  \[2x+y\]               done clear
  B)
                  \[x+2y\] done clear
  C)
                  \[2x+2y\]             done clear
  D)
                  \[8x+10y\] done clear
  View Solution play_arrow

• question_answer41)
  In a test of Mathematics, there are two types of questions to be answered?short answered and long answered. The relevant data is given below

  Type of questions		Time taken to solve	Marks	Number of questions
  	Short answered questions	5 minute	3	10
  	Long answered questions	10 minute	5	14

  The total marks is 100. Students can solve all the questions. To secure maximum marks, a student solves x short answered and y long answered questions in three hours, then the linear constraints except\[x\ge 0,\ y\ge 0\], are
  A)
                  \[5x+10y\le 180\], \[x\le 10,\ y\le 14\] done clear
  B)
                  \[x+10y\ge 180\], \[x\le 10,\ y\le 14\] done clear
  C)
                  \[5x+10y\ge 180\], \[x\ge 10,\ y\ge 14\] done clear
  D)
                  \[5x+10y\le 180\], \[x\ge 10,\ y\ge 14\] done clear
  View Solution play_arrow

• question_answer42)
  The objective function for the above question is
  A)
                  \[10x+14y\]        done clear
  B)
                  \[5x+10y\] done clear
  C)
                  \[3x+5y\]             done clear
  D)
                  \[5y+3x\] done clear
  View Solution play_arrow

• question_answer43)
  The vertices of a feasible region of the above question are 
  A)
                  (0, 18), (36, 0)    done clear
  B)
                  (0, 18), (10, 13) done clear
  C)
                  (10, 13), (8, 14)  done clear
  D)
                  (10, 13), (8, 14), (12, 12) done clear
  View Solution play_arrow

• question_answer44)
  The maximum value of objective function in the above question is 
  A)
                  100         done clear
  B)
                  92 done clear
  C)
                  95           done clear
  D)
                  94 done clear
  View Solution play_arrow

• question_answer45)
  A factory produces two products A and B. In the manufacturing of product A, the machine and the carpenter requires 3 hour each and in manufacturing of product B, the machine and carpenter requires 5 hour and 3 hour respectively. The machine and carpenter work at most 80 hour and 50 hour per week respectively. The profit on A and B is Rs. 6 and 8 respectively. If profit is maximum by manufacturing x and y units of A and B type product respectively, then for the function \[6x+8y\] the constraints are   
  A)
                  \[x\ge 0,\ y\ge 0,\ 5x+3y\le 80,\ 3x+2y\le 50\] done clear
  B)
                  \[x\ge 0,\ y\ge 0,\ 3x+5y\le 80,\ 3x+3y\le 50\] done clear
  C)
                  \[x\ge 0,\ y\ge 0,\ 3x+5y\ge 80,\ 2x+3y\ge 50\] done clear
  D)
                  \[x\ge 0,\ y\ge 0,\ 5x+3y\ge 80,\ 3x+2y\ge 50\] done clear
  View Solution play_arrow

• question_answer46)
  A shopkeeper wants to purchase two articles A and B of cost price Rs. 4 and 3 respectively. He thought that he may earn 30 paise by selling article A and 10 paise by selling article B. He has not to purchase total article worth more than Rs. 24. If he purchases the number of articles of A and B, x and y respectively, then linear constraints are 
  A)
                  \[x\ge 0,\ y\ge 0,\ 4x+3y\le 24\]               done clear
  B)
                  \[x\ge 0,\ y\ge 0,\ 30x+10y\le 24\] done clear
  C)
                  \[x\ge 0,\ y\ge 0,\ 4x+3y\ge 24\]              done clear
  D)
                  \[x\ge 0,\ y\ge 0,\ 30x+40y\ge 24\] done clear
  View Solution play_arrow

• question_answer47)
  In the above question the is o-profit line is 
  A)
                  \[3x+y=30\]        done clear
  B)
                  \[x+3y=20\] done clear
  C)
                  \[3x-y=20\]         done clear
  D)
                  \[4x+3y=24\] done clear
  View Solution play_arrow

• question_answer48)
  The sum of two positive integers is at most 5. The difference between two times of second number and first number is at most 4. If the first number is x and second number y, then for maximizing the product of these two numbers, the mathematical formulation is 
  A)
                  \[x+y\ge 5\], \[2y-x\ge 4,\ \ x\ge 0,\ y\ge 0\] done clear
  B)
                  \[x+y\ge 5\], \[-2x+y\ge 4,\ \ x\ge 0,\ y\ge 0\] done clear
  C)
                  \[x+y\le 5\], \[2y-x\le 4,\ \ x\ge 0,\ y\ge 0\] done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer49)
  For the L.P. problem Max\[z=3{{x}_{1}}+2{{x}_{2}}\] such that \[2{{x}_{1}}-{{x}_{2}}\ge 2\], \[{{x}_{1}}+2{{x}_{2}}\le 8\] and \[{{x}_{1}},\ {{x}_{2}}\ge 0\], \[z=\]
  A)
                  12           done clear
  B)
                  24 done clear
  C)
                  36           done clear
  D)
                  40 done clear
  View Solution play_arrow

• question_answer50)
  For the L.P. problem Min\[z=-{{x}_{1}}+2{{x}_{2}}\] such that \[-{{x}_{1}}+3{{x}_{2}}\le 0,\]\[{{x}_{1}}+{{x}_{2}}\le 6,\ {{x}_{1}}-{{x}_{2}}\le 2\]and \[{{x}_{1}},\ {{x}_{2}}\ge 0\],\[{{x}_{1}}=\]
  A)
                  2              done clear
  B)
                  8 done clear
  C)
                  10           done clear
  D)
                  12 done clear
  View Solution play_arrow

• question_answer51)
  For the L.P. problem Min\[z={{x}_{1}}+{{x}_{2}}\] such that \[5{{x}_{1}}+10{{x}_{2}}\le 0,\ \ {{x}_{1}}+{{x}_{2}}\ge 1,\ \ {{x}_{2}}\le 4\] and \[{{x}_{1}},\ {{x}_{2}}\ge 0\]
  A)
                  There is a bounded solution        done clear
  B)
                  There is no solution done clear
  C)
                  There are infinite solutions done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer52)
  On maximizing \[z=4x+9y\] subject to \[x+5y\le 200,\]  \[x+5y\le 200,\ \ 2x+3y\le 134\] and \[x,\ y\ge 0\], \[z=\]                
  A)
                  380         done clear
  B)
                  382 done clear
  C)
                  384         done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer53)
  For the L.P. problem Min\[z=2x+y\] subject to \[5x+10y\le 50,\] \[x+y\ge 1,\ \ y\le 4\] and \[x,\ y\ge 0\], \[z=\]
  A)
                  0              done clear
  B)
                  1 done clear
  C)
                  2              done clear
  D)
                  ½ done clear
  View Solution play_arrow

• question_answer54)
  For the L.P. problem Min\[z=2x-10y\] subject to \[x-y\ge 0,\ \ x-5y\ge -5\] and \[x,\ y\ge 0\], \[z=\]
  A)
                  ?10         done clear
  B)
                  ?20 done clear
  C)
                  0              done clear
  D)
                  10 done clear
  View Solution play_arrow

• question_answer55)
  The point at which the maximum value of \[(3x+2y)\] subject to the constraints \[x+y\le 2,\ x\ge 0,\ y\ge 0\] is obtained, is          [MP PET 1993]
  A)
                  (0, 0)      done clear
  B)
                  (1.5, 1.5) done clear
  C)
                  (2, 0)      done clear
  D)
                  (0, 2) done clear
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• question_answer56)
  The minimum value of objective function \[c=2x+2y\] in the given feasible region, is 
  A)
                  134         done clear
  B)
                  40 done clear
  C)
                  38           done clear
  D)
                  80 done clear
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• question_answer57)
  The minimum value of linear objective function \[c=2x+2y\] under linear constraints \[3x+2y\ge 12\], \[x+3y\ge 11\]  and \[x,\ y\ge 0\], is 
  A)
                  10           done clear
  B)
                  12 done clear
  C)
                  6              done clear
  D)
                  5 done clear
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• question_answer58)
  The solution for minimizing the function \[z=x+y\] under a L.P.P. with constraints \[x+y\ge 1\], \[x+2y\le 10\], \[y\le 4\] and \[x,\ y\ge 0\],  is 
  A)
                  \[x=0,\ y=0,\ z=0\]          done clear
  B)
                  \[x=3,\ y=3,\ z=6\] done clear
  C)
                  There are infinitely solutions      done clear
  D)
                  None of these done clear
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• question_answer59)
  The solution of a problem to maximize the objective function \[z=x+2y\] under the constraints \[x-y\le 2\], \[x+y\le 4\] and \[x,\ y\ge 0\], is 
  A)
                  \[x=0,\ y=4,\ z=8\]          done clear
  B)
                  \[x=1,\ y=2,\ z=5\] done clear
  C)
                  \[x=1,\ y=4,\ z=9\]          done clear
  D)
                  \[x=0,\ y=3,\ z=6\] done clear
  View Solution play_arrow

• question_answer60)
  To maximize the objective function \[z=2x+3y\] under the constraints \[x+y\le 30,\ x-y\ge 0,\ y\le 12,\] \[x\le 20,\] \[y\ge 3\] and \[x,\ y\ge 0\]
  A)
                  \[x=12,\ y=18\] done clear
  B)
                  \[x=18,\ y=12\] done clear
  C)
                  \[x=12,\ y=12\] done clear
  D)
                  \[x=20,\ y=10\] done clear
  View Solution play_arrow

• question_answer61)
  The maximum value of \[P=6x+8y\] subject to constraints \[2x+y\le 30,\ x+2y\le 24\] and \[x\ge 0,\ y\ge 0\] is  [MP PET 1994; 95]
  A)
                  90           done clear
  B)
                  120 done clear
  C)
                  96           done clear
  D)
                  240 done clear
  View Solution play_arrow

• question_answer62)
  The maximum value of \[P=x+3y\] such that \[2x+y\le 20\], \[x+2y\le 20\], \[x\ge 0,\ y\ge 0\], is              [MP PET 1995]
  A)
                  10           done clear
  B)
                  60 done clear
  C)
                  30           done clear
  D)
                  None of these done clear
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• question_answer63)
  The maximum value of \[z=4x+2y\] subject to the constraints \[2x+3y\le 18,\ x+y\ge 10\]; \[x,\ y\ge 0\], is  [MP PET 2001]
  A)
                  36           done clear
  B)
                  40 done clear
  C)
                  20           done clear
  D)
                  None of these done clear
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• question_answer64)
  \[z=ax+by,\ a,\ b\] being positive, under constraints \[y\ge 1\], \[x-4y+8\ge 0\], \[x,\ y\ge 0\] has  
  A)
                  Finite maximum               done clear
  B)
                  Finite minimum done clear
  C)
                  An unbounded minimum solution done clear
  D)
                  An unbounded maximum solution done clear
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• question_answer65)
  By graphical method, the solution of linear programming problem Maximize \[z=3{{x}_{1}}+5{{x}_{2}}\] Subject to \[3{{x}_{1}}+2{{x}_{2}}\le 18\], \[{{x}_{1}}\le 4\], \[{{x}_{2}}\le 6\],\[{{x}_{1}}\ge 0\],\[{{x}_{2}}\ge 0\] is             [MP PET 1996]
  A)
                  \[{{x}_{1}}=2,\ {{x}_{2}}=0,\ z=6\]            done clear
  B)
                  \[{{x}_{1}}=2,\ {{x}_{2}}=6,\ z=36\] done clear
  C)
                  \[{{x}_{1}}=4,\ {{x}_{2}}=3,\ z=27\]          done clear
  D)
                  \[{{x}_{1}}=4,\ {{x}_{2}}=6,\ z=42\] done clear
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• question_answer66)
  The point at which the maximum value of \[(x+y)\] subject to the constraints \[2x+5y\le 100\], \[\frac{x}{25}+\frac{y}{49}\le 1\], \[x,\ y\ge 0\] is obtained, is 
  A)
                  (10, 20) done clear
  B)
                  (20, 10) done clear
  C)
                  (15, 15) done clear
  D)
                  \[\left( \frac{50}{3},\ \frac{40}{3} \right)\] done clear
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• question_answer67)
  The maximum value of \[(x+2y)\] under the constraints \[2x+3y\le 6,\ x+4y\le 4,\ \ x,\ y\ge 0\] is
  A)
                  3              done clear
  B)
                  3.2 done clear
  C)
                  2              done clear
  D)
                  4 done clear
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• question_answer68)
  The maximum value of \[10x+5y\] under the constraints \[3x+y\le 15,\ x+2y\le 8,\] \[x,\ y\ge 0\] is 
  A)
                  20           done clear
  B)
                  50 done clear
  C)
                  53           done clear
  D)
                  70 done clear
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• question_answer69)
  The point at which the maximum value of \[(x+y)\], subject to the constraints \[x+2y\le 70,\ 2x+y\le 95\], \[x,\ y\ge 0\] is obtained, is  
  A)
                  (30, 25) done clear
  B)
                  (20, 35) done clear
  C)
                  (35, 20) done clear
  D)
                  (40, 15) done clear
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• question_answer70)
  If \[3{{x}_{1}}+5{{x}_{2}}\le 15\], \[5{{x}_{1}}+2{{x}_{2}}\le 10\], \[{{x}_{1}},\ {{x}_{2}}\ \ \ge 0\]                 then the maximum value of \[5{{x}_{1}}+3{{x}_{2}}\], by graphical method is
  A)
                  \[12\frac{7}{19}\]             done clear
  B)
                  \[12\frac{1}{7}\] done clear
  C)
                  \[12\frac{3}{5}\]               done clear
  D)
                  12 done clear
  View Solution play_arrow

• question_answer71)
  The maximum value of \[z=5x+2y\], subject to the constraints \[x+y\le 7,\ x+2y\le 10\], \[x,\ y\ge 0\] is                  [AMU 1999]
  A)
                  10           done clear
  B)
                  26 done clear
  C)
                  35           done clear
  D)
                  70 done clear
  View Solution play_arrow

• question_answer72)
  The maximum value of \[z=3x+4y\] subject to the constraints \[x+y\le 40,\ x+2y\le 60,\ x\ge 0\] and \[y\ge 0\] is                   [MP PET 2002, 04]
  A)
                  120         done clear
  B)
                  140 done clear
  C)
                  100         done clear
  D)
                  160 done clear
  View Solution play_arrow

• question_answer73)
  The minimum value of\[z=2{{x}_{1}}+3{{x}_{2}}\] subject to the constraints\[2{{x}_{1}}+7{{x}_{2}}\ge 22\],\[{{x}_{1}}+{{x}_{2}}\ge 6\],\[5{{x}_{1}}+{{x}_{2}}\ge 10\] and \[{{x}_{1}},\ {{x}_{2}}\ge 0\] is              [MP PET 2003]
  A)
                  14           done clear
  B)
                  20 done clear
  C)
                  10           done clear
  D)
                  16 done clear
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• question_answer74)
  The co-ordinates of the point for minimum value of \[z=7x-8y\]subject to the conditions\[x+y-20\le 0\], \[y\ge 5,\,\] \[x\ge 0\], \[y\ge 0\] is [DCE 2005]
  A)
                  (20, 0)   done clear
  B)
                  (15, 5) done clear
  C)
                  (0, 5)      done clear
  D)
                  (0, 20) done clear
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• question_answer75)
  The maximum value of \[\mu =3x+4y\], subject to the conditions \[x+y\le 40,x+2y\le 60,x,y\ge 0\] is                                 [MP PET 2004]
  A)
                  130         done clear
  B)
                  120 done clear
  C)
                  40           done clear
  D)
                  140 done clear
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