JEE Main & Advanced
Mathematics
Linear Programming
Question Bank
Critical Thinking
question_answer
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 \[{{x}_{1}},\ {{x}_{2}}\ge 0\]
A)\[{{x}_{1}}=1.2\]
B)\[{{x}_{2}}=2.6\]
C)\[z=10.2\]
D)All the above
Correct Answer:
D
Solution :
The graph of linear programming problem is as given below
Hence the required feasible region is given by the graph whose vertices are\[A\,(1.2,\,2.6),B(4.5,\,1.5)\]and\[C\,\left( \frac{8}{3},\frac{10}{3} \right)\]
Thus objective function is minimum at \[A\,(1.2,\,2.6)\]
So \[{{x}_{1}}=1.2,\,{{x}_{2}}=2.6\]and\[z=2\times 1.2+3\times 2.6=10.2\].