Question

A factory makes 3 components, A, B and C using the same production process for each. A unit of A take 1hr, a unit of B takes 0.75hrs and a unit of C takes 0.5hrs. In addition, C has to be hand finished, an activity taking 0.25hrs per unit. Each week total production time (excluding hand finishing) must not exceed 300hrs and hand finishing must not exceed 45 hrs. The components are finally assembled to make two finished products. One product consists of 1 unit of A and 1 unit of C selling for 30 pounds whilst the other consists of 2 units of B and 1 unit of C and sells for 45 pounds. At most 130 of the first product and 100 of the second product can be sold each week. Formulate the problem of planning weekly production to maximise total proceeds as a linear programming problem.

Answer 1

The problem can be formulated as a linear programming problem to maximize total proceeds. The objective is to maximize total proceeds, and constraints are set based on the production time and hand finishing time for each component. Using the linear programming model, the optimal production quantities can be determined.

Step-by-step explanation:

The problem can be formulated as a linear programming problem to maximize total proceeds. Let's define the decision variables:

• x1 = Number of units of A produced
• x2 = Number of units of B produced
• x3 = Number of units of C produced

The objective is to maximize total proceeds, which can be represented as:

Maximize P = 30x1 + 45x2

Subject to the following constraints:

1. x1 + x3 ≤ 130
2. 2x2 + x3 ≤ 100
3. 1x1 + 0.75x2 + 0.5x3 ≤ 300
4. 0.25x3 ≤ 45
5. All variables x1, x2, x3 ≥ 0

Using the above objective function and constraints, we can solve this linear programming problem to determine the optimal production quantities of each component.