question_answer

To maximize the objective function \[z=2x+3y\] under the constraints \[x+y\le 30,\ x-y\ge 0,\ y\le 12,\] \[x\le 20,\] \[y\ge 3\] and \[x,\ y\ge 0\]

A)                 \[x=12,\ y=18\]

B)                 \[x=18,\ y=12\]

C)                 \[x=12,\ y=12\]

D)                 \[x=20,\ y=10\]

Correct Answer: B

Solution :

                The objective function is Max\[z=2x+3y\].                 The vertices are \[A(20,\,10)\], \[B(18,\,12),C(12,\,12),D\]\[(3,\,3)\] and E (20, 3). Hence the maximum value of the objective function will be at (18, 12).