(i) From the figure the feasible region is OABC. Then the comer points are; A is (5, 0), B is (3, 4), C is (0, 5) and O (0, 0)
(ii) The constraints are 2x + y < 10, x + 3y < 15, x < 0, y < 0
(iii) Given; Z = px + qy
Corner points |
Value of Z |
O |
Z=p(0)+q(0) = 0 |
A |
Z = p(5) + q(Q) = 5p |
B |
Z = p( 3)+g(4) = 3p + 4q |
C |
Z = p(0) + q(5) = 5q |
Since maximum at A and B we have;
⇒ 3p + 4q = 5p ⇒ 2p = 4q ⇒ p = 2q
(iv) When q = 1, then p ⇒ 2q ⇒ p = 2
Objective function is; Z = 2x + y
(v) We have; Z px + qy at B Z has maximum
⇒ Z = 2(3) + 4
= 10