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question_answer1) For the following shaded area, the linear constraints except \[x\ge 0\] and \[y\ge 0\], are
question_answer2) In equations \[3x-y\ge 3\] and \[4x-y>4\] [MP PET 2001]
question_answer3) Shaded region is represented by [MP PET 1997]
question_answer4) A Firm makes pents and shirts. A shirt takes 2 hour on machine and 3 hour of man labour while a pent takes 3 hour on machine and 2 hour of man labour. In a week there are 70 hour machine and 75 hour of man labour available. If the firm determine to make x shirts and y pents per week, then for this the linear constraints are
question_answer5) For the L.P. problem Min\[z=2{{x}_{1}}+3{{x}_{2}}\] such that \[-{{x}_{1}}+2{{x}_{2}}\le 4,\] \[{{x}_{1}}+{{x}_{2}}\le 6,\ \ {{x}_{1}}+3{{x}_{2}}\ge 9\] and \[{{x}_{1}},\ {{x}_{2}}\ge 0\]
question_answer6) A company manufactures two types of products A and B. The storage capacity of its godown is 100 units. Total investment amount is Rs. 30,000. The cost price of A and B are Rs. 400 and Rs. 900 respectively. If all the products have sold and per unit profit is Rs. 100 and Rs. 120 through A and B respectively. If x units of A and y units of B be produced, then two linear constraints and iso-profit line are respectively
question_answer7) The L.P. problem Max\[z={{x}_{1}}+{{x}_{2}}\] such that \[-2{{x}_{1}}+{{x}_{2}}\le 1,\ {{x}_{1}}\le 2,\ {{x}_{1}}+{{x}_{2}}\le 3\] and \[{{x}_{1}},\ {{x}_{2}}\ge 0\] has
question_answer8) The minimum value of the objective function \[z=2x+10y\] for linear constraints \[x\ge 0,\ y\ge 0\], \[x-y\ge 0\], \[x-5y\le -5\], is
question_answer9) The maximum value of \[z=4x+3y\] subject to the constraints \[3x+2y\ge 160,\ 5x+2y\ge 200\], \[x+2y\ge 80\]; \[x,\ y\ge 0\] is [MP PET 1998]
question_answer10) Minimize \[z=\sum\limits_{j=1}^{n}{{}}\sum\limits_{i=1}^{m}{{{c}_{ij}}\,{{x}_{ij}}}\] Subject to : \[\sum\limits_{j=1}^{n}{{{x}_{ij}}\le {{a}_{i}},\ i=1,.......,m}\] \[\sum\limits_{i=1}^{m}{{{x}_{ij}}={{b}_{j}},\ j=1,......,n}\] is a (L.P.P.) with number of constraints [MP PET 1999]
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