question_answer

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          

B)                 120

C)                 96          

D)                 240

Correct Answer: B

Solution :

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