A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below. The decision variables are defined as X_i = the amount of product i produced
Y_i = 1 if X_i > 0 and 0 if X_i = 0
What is the objective function for this problem?

Question

A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below.

The decision variables are defined as X_i = the amount of product i produced
Y_i = 1 if X_i > 0 and 0 if X_i = 0
What is the objective function for this problem?

Quizplus · Accepted Answer

The objective function is to maximize profit. The total profit is the sum of the profit from producing each unit of product, which is 17 X₁ + 21 X₂. However, there are setup costs associated with each batch, so we need to subtract the setup costs for the batches that are produced, which is 60 Y₁ + 80 Y₂. Therefore, the objective function is MAX: 17 X₁ + 21 X₂ − 60 Y₁ − 80 Y₂.

A Company Is Developing Its Weekly Production Plan