# The purpose of this exercise is to discuss the situation facing a manager and help the manager

## Question:

The purpose of this exercise is to discuss the situation facing a manager and help the manager determine the product mix (quantities of each product) that maximizes profitability.

A fundamental decision for a manufacturing company is the product mix decision, which consists of the quantity of each product to make in order to maximize profitability (or minimize losses) for the organization. XYZ Corp. manufactures five different products: A, B, C, D and E. Table 1 presents the product prices, material costs, and weekly demand. Table 2 presents the labor requirements and labor availability for each of the four work centers in the XYZ manufacturing plant. The labor requirements indicate how much labor time is required to manufacture one unit of each product. The available labor indicates that two full-time employees each are assigned to work centers 1 and 4. Work center 2 has one full-time employee, while work center 3 has three full-time employees. In order to simplify the problem, assume that setup times in the work centers and efficiencies are not relevant. Total operating expenses per week are \$14,000 (not including cost of materials).

1. Determine which work center is the constraint by calculating the total production time needed to manufacture the weekly demand of each product.

The constraint is work center ______________.

2. What is the throughput and throughput per constraint minute for each product?

3. How much of each product should we manufacture to maximize profitability? What will our weekly profit be for this product mix? (You must show the order of the production choices you made to receive full credit.)

4. How would you explain the logic of your decision to management? Consider the usual procedure for product mix decisions in your response.

5. Now that you have convinced management that we should use the Theory of Constraints to make product mix decisions, you have been asked to help them understand the impact of elevating the constraint. If we could add more labor to the constraint work center, how much would our throughput change based on time added? What is the maximum hourly rate that we would be willing to pay?

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