question_answer

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          

B)                 24

C)                 36          

D)                 40

Correct Answer: B

Solution :

 Change the inequalities into equations and draw the graph of lines, thus we get the required feasible region.                 It is a bounded region, bounded by the vertices \[A(1,0),B\,(8,0)\] and \[C\,\left( \frac{12}{5},\frac{14}{5} \right)\]. Now by evaluation of the objective function for the vertices of feasible region it is found to be maximum at (8,0). Hence the solution is \[z=3\times 8+0\times 2=24\].