Question

The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let z = px + qy, where p, q > 0. Condition on p and q so that the maximum of z occurs at both the point (15, 15) and (0, 20) is
(a) p = q
(b) p = 2q
(c) q = 2p
(d) q = 3p

Answer 1

Since the maximum value is obtained at (15, 15) and (0, 20)
But maximum value obtained is unique
∴ Z_max = p(15) + q(15) = 15p + 15q
and Z_max = p(0) + (20) = 0 + 20q
i.e. 15p + 15q = 20q
i.e. 15p = 5q
i.e. 3p = q
Hence, the correct answer is option D.