Question

The corner points of the bounded feasible region of an LPP are O(0, 0), A(250, 0), B(200, 50) and C(0, 175). If the maximum value of the objective function Z = 2ax + by occurs at the points A(250, 0) and B(200, 50), then the relation between a and b is :

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.