Question

Find the minimum value of C = 2x + y subject to the following constraints:

2x + 3y ≥ 24
4x + y ≥ 38
x ≥ 0
y ≥ 0
A) C = 38
B) C = 24
C) C = 17
D) C = 0

Answer 1

The minimum value of the objective function C = 2x + y is 24

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 = 2x + y

Subject to the constraints:

2x + 3y ≥ 24

4x + y ≥ 38

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) = (12, 0)

Recall that

C = 2x + y

So, we have

C = 2 * 12 + 0 = 24

Hence, the minimum value of the objective function is 24