Question

Formulate a linear programming model for a department to maximize total profit contribution. Define the variables and constraints. (Pj = units of product i produced, for i=1,2,3)

Answer 1

To maximize total profit contribution, the linear programming model involves defining variables and constraints. The objective is to maximize the total profit contribution represented by a linear equation, subject to non-negativity and resource constraints.

Step-by-step explanation:

To formulate a linear programming model for maximizing total profit contribution, we need to define the variables and constraints. Let P1, P2, and P3 represent the units of products 1, 2, and 3 produced, respectively. The objective is to maximize the total profit contribution, which can be represented as:

Maximize Z = 10P1 + 15P2 + 20P3

Subject to the following constraints:

1. P1 ≥ 0 (non-negativity constraint)
2. P2 ≥ 0 (non-negativity constraint)
3. P3 ≥ 0 (non-negativity constraint)
4. 2P1 + 3P2 + 4P3 ≤ 100 (resource constraint)
5. 3P1 + 2P2 + 5P3 ≤ 120 (resource constraint)