Q. 175.0( 1 Vote )

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

2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (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 :

Given the vertices of the feasible region are:

O (0,0)

A (5,0)

B (3,4)

C (0,5)

Also given the objective function is Z = px+qy

Now substituting O,A,B and C in Z

As per the condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5)

Then we can equate Z values at B and C, this gives

3p + 4q = 5q

3p = 5q – 4q

3p = q

Therefore the answer is option D i.e. q = 3p.

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