Question: Find the point at which the maximum value of the objective function P = 4x + 9y subject to the constraints x ≥ 0,y ≥ 0 and 3x + y ≤ 6 occurs.
A ) (0, 6) B ) (1, 6) C ) (0, 0) D ) (0, 2)
Steps to derive
1 Objective function is P = 4x + 9y
2 Constraints are x ≥ 0, y ≥ 0and 3x + y ≤ 6
3 The feasible region determined by the given constraints is shown.
4 From the graph the vertices are (0, 0), (2, 0) and (0, 6).
5 To find the minimum and maximum values of P, we evaluate P = 4x + 9y at each of the vertices.
6 At (0, 0), P = 4(0) + 9(0) = 0 [Substitute the values.]
7 At (2, 0), P = 4(2) + 9(0) = 8 [Substitute the values.]
8 At (0, 6), P = 4(0) + 9(6) = 54 [Substitute the values.]
9 So, the maximum value of P is 54 which occurs when x = 0, y = 6.
