question_answer

The maximum value of \[z=6x+8y\] subject to constraints \[2x+y\le 30,x+2y\le 24\] and \[x\ge 0,y\ge 0\] is

A) 90

B) 120

C) 96

D) 240

Correct Answer: B

Solution :

[b] Here, \[2x+y\le 30,x+2y\le 24,x,y\ge 0\] The shaded region represents the feasible region, hence \[z=6x+8y.\] Obviously it is maximum at \[(12,6).\] Hence \[z=12\times 6+8\times 6=120\]