Question

Given the following linear optimization model, transform the constraints:

Maximize Z = 3x + 2y
Subject to 2x + y ≤ 20
4x - 5y ≥ -10
x, y ≥ 0
a. 2x + y ≤ 20, 4x - 5y ≥ -10, x ≥

Answer 1

To transform the constraints in the given linear optimization model, multiply the second constraint by -1 and leave the first and third constraints unchanged.

Step-by-step explanation:

The given linear optimization model is:

Maximize Z = 3x + 2y

Subject to:

2x + y ≤ 20

4x - 5y ≥ -10

x, y ≥ 0

In order to transform the constraints:

1. The first constraint is already in the correct form.
2. For the second constraint, we can multiply both sides by -1 to change the direction of the inequality, giving -4x + 5y ≤ 10.
3. The third constraint is already in the correct form.

Therefore, the transformed constraints are:

2x + y ≤ 20

-4x + 5y ≤ 10

x, y ≥ 0