Question

26. The corner points of the feasible region determined by the system of linear constraints are
(0,3),(1,1),(3,0). Let Z=px+qy, where p,q>0, condition on p and q so that the minimum of Zoccurs at
the points (3,0) and (1,1) is
a) P=2q
b) p=
c) p=3q
62 / 2
d) q=p
​

Answer 1

Step-by-step explanation:

Let z

0

be the maximum value of z in the feasible region.

Since maximum occurs at both (15,15) and (0,20)$, the value z

0

is attained at both (15,15) and (0,20).

⟹z

0

=p(15)+q(15) and z

0

=p(0)+q(20)

⟹p(15)+q(15)=p(0)+q(20)

⟹15p=5q

⟹3p=q

Hence, the answer is option (D).