Question

In the graph, the feasible region representing the Linear Programming Problem for maximising objective function Z = px + qy, p, q > 0 is shaded. If all points on segment AB give max (Z), then which of the following is true ?

Solve the following Linear Programming Problem graphically : Maximise Z = 200x + 120y subject to the constraints x + y ≤ 300 3x + y ≤ 600 x − y ≥ −100 x, y ≥ 0

Assertion (A) : Consider a Linear Programming Problem with minimise Z = x + 2y subject to constraints 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0 which gives minimum Z at infinitely many points. The corner points of feasible region are (0, 3) and (6, 0). Reason (R) : If two corner points produce the same minimum value of the objective function, then every point on the line segment joining the points will give the same minimum value.

In an LPP, if the objective function has the same minimum value on two corner points of the feasible region, then the number of points at which the minimum value of objective function occurs is :