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
Which of the following constraints creates the link between setting up to produce A's and making some A's 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
Which of the following constraints creates the link between setting up to produce A's and making some A's for this problem?

Quizplus · Accepted Answer

Constraint A links the amount of A produced to the setup cost for A. Specifically, if X₁ is greater than 0 (indicating that A is being produced), then the setup cost for A must be less than or equal to 16 (the total setup cost available). This ensures that the company is using its setup resources efficiently and only setting up for A when it makes financial sense to do so.

A Company Is Developing Its Weekly Production Plan