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For the objective function z = px + qy, where p, q > 0 the corner points of the feasible region determined by the system of linear constraints are
Question

For the objective function z = px + qy, where p, q > 0 the corner points of the feasible region determined by the system of linear constraints are - (0, 10), (5, 5), (15, 15) and (0, 20), condition on p and q so that maximum of z occurs at both the points (15, 15) and (0, 20) is:

A.

p=q

B.

p=2q

C.

q =2р

D.

q =3р

Correct option is D

Given
z=px+qy
Corner points are (0, 10), (5, 5), (15, 15) & (0, 20). Then, ATQ.
15p+15q=20q
15p=5q
3p=q

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