. 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\[(12,\,\,6)\].