Question

Suppose we have the following minimization problem: minimize: c(x, y) = 4x - 7y, subject to: x-y≥ 1, 3x - 2y ≤ 18, x ≥ 0, y ≥ 0. Find the minimum value of c graphically.

Answer 1

The minimum value of the objective function C(x, y) = 4x - 7y is -41

How to find the minimum value of the objective function

From the question, we have the following parameters that can be used in our computation:

C(x, y) = 4x - 7y

Subject to:

x - y ≥ 1

3x - 2y ≤ 18

x ≥ 0

y ≥ 0

The graph of the constraints is added as an attachment

From the graph, we have the following feasible points

(x, y) = (1, 0), (6, 0) and (16, 15)

Recall that

C(x, y) = 4x - 7y

So, we have

C(1, 0) = 4(1) - 7(0) = 4

C(6, 0) = 4(6) - 7(0) = 24

C(16, 15) = 4(16) - 7(15) = -41

Hence, the minimum value of the objective function is -41