Question

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) .Find the relation,

Answer 1

The maximum value of Z is unique.

It is given that the maximum value of Z occurs at two points, (3, 4) and(0,5).

therefore Value of Z at (3, 4) = Value of Z at =(0,5)

=>p(3) + q(4) = p(0) + q(5)

=>3p + 4q = 5g

=>q = 3p