Question

The corner points of the feasible region are determined by the following system of linear inequalities:
2x+y≤10,x+3y≤15,xy≥0 are (0,0),(5,0),(3,4)and(0,5)Let Z=px+qy,where p,q >0.Condition on p and q so that the maximum of Z occurs at both (3,4)and (0,5) is

• A. p=q
• B. p=2q
• C. p=3q
• D. q=3p

Answer 1

Answer: (D)

q=3p

Answer 2

The maximum value of Z is unique.

It is given that the maximum value of Z occurs at two points, (3,4) and (0,5).

∴Value of Z at (3,4)=Value of Z at (0,5).

$\Rightarrow$p(3)+q(4)=p(0)+q(5)

$\Rightarrow$3p+4p=5q
$\Rightarrow$q=3p

Hence,the correct answer is D.