question_answer

The maximum value of \[z=3x+4y\] subject to the constraints \[x+y\le 40,\ x+2y\le 60,\ x\ge 0\] and \[y\ge 0\] is                   [MP PET 2002, 04]

A)                 120        

B)                 140

C)                 100        

D)                 160

Correct Answer: B

Solution :

                Given, \[P=3x+4y\]                                 This graph has been draw from given constraints and maximum value of P will be at A or B or C .                                 \[{{P}_{A}}={{P}_{(0,30)}}=3\times 0+4\times 30=120\]                                 \[{{P}_{B}}={{P}_{(20,20)}}=3\times 20+4\times 20=140\]                                 \[{{P}_{C}}={{P}_{(40,0)}}=3\times 40+0=120\] Therefore \[{{P}_{\max }}=140\].