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

A) \[90\]                                   

B) \[120\]

C) \[96\]                                   

D) \[240\]

Correct Answer: B

Solution :

Feasible region of constraints is shown in the graph. Extreme points are\[(0,\,\,0),\,\,\,(15,\,\,0),\,\,\,(0,\,\,12)\]and\[(12,\,\,6)\]. Since,\[P=6x+8y\]                 \[{{P}_{(12,\,\,6)}}=72+48=120\]                 \[{{P}_{(0,\,\,0)}}=0\]                 \[{{P}_{(15,\,\,0)}}=90+0=90\]                 \[{{P}_{(0,\,\,12)}}=0+96=96\] Clearly, maximum value of\[P\]is\[120\]at\[(12,\,\,6)\].