Question

The corner points of the feasible region determined by the following system of linear inequalities :

$2x+y\ge 10,x+3y\ge 15,x,y\ge 0are(0,0),(5,0),(3,4)and(0,5).$ 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

(d) 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)

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

Hence, option (d) is correct.