Table 5.3
King Supply makes four different types of plumbing fixtures: W, X, Y and Z. The contribution margins for these products are: $70 for Product W, $60 for Product X, $90 for Product Y and $100 for Product Z. Fixed overhead is estimated at $5,500 per week. The manufacture of each fixture requires four machines, Machines #1, 2, 3 and 4. Each of the machines is available for 40 hours a week and there is no setup time required when shifting from the production of one product to any other. The processing requirements to make one unit of each product are shown in the table. Weekly product demand for the next planning period has been forecasted as follows: 70 Ws, 60 Xs, 50 Ys and 30 Zs.

In the questions that follow, the traditional method refers to maximizing the contribution margin per unit for each product, and the bottleneck method refers to maximizing the contribution margin per minute at the bottleneck for each product.
-Use the information in Table 5.3. Using the bottleneck method, what is the optimal product mix?
A) 70 W, 60 X, 90 Y, 100 Z
B) 70 W, 50 X, 50 Y, 30 Z
C) 70 W, 60 X, 47 Y, 30 Z
D) 70 W, 47 X, 50 Y, 30 Z

Question

Table 5.3
King Supply makes four different types of plumbing fixtures: W, X, Y and Z. The contribution margins for these products are: $70 for Product W, $60 for Product X, $90 for Product Y and $100 for Product Z. Fixed overhead is estimated at $5,500 per week. The manufacture of each fixture requires four machines, Machines #1, 2, 3 and 4. Each of the machines is available for 40 hours a week and there is no setup time required when shifting from the production of one product to any other. The processing requirements to make one unit of each product are shown in the table. Weekly product demand for the next planning period has been forecasted as follows: 70 Ws, 60 Xs, 50 Ys and 30 Zs.
  
In the questions that follow, the traditional method refers to maximizing the contribution margin per unit for each product, and the bottleneck method refers to maximizing the contribution margin per minute at the bottleneck for each product.
-Use the information in Table 5.3. Using the bottleneck method, what is the optimal product mix?
A) 70 W, 60 X, 90 Y, 100 Z 
B) 70 W, 50 X, 50 Y, 30 Z 
C) 70 W, 60 X, 47 Y, 30 Z 
D) 70 W, 47 X, 50 Y, 30 Z

Quizplus · Accepted Answer

To use the bottleneck method, we need to calculate the contribution margin per minute for each product. The machine with the lowest number of available hours is the bottleneck machine, which is Machine #4. It is available for 28,800 minutes per week (40 hours x 60 minutes).

The processing time for each product on Machine #4 is:

- Product W: 1 minute per unit
- Product X: 3 minutes per unit
- Product Y: 2 minutes per unit
- Product Z: 4 minutes per unit

To calculate the contribution margin per minute, we divide the contribution margin per unit by the processing time on Machine #4:

- Product W: $70 / 1 minute = $70 per minute
- Product X: $60 / 3 minutes = $20 per minute
- Product Y: $90 / 2 minutes = $45 per minute
- Product Z: $100 / 4 minutes = $25 per minute

Therefore, the optimal product mix would be the one that maximizes the contribution margin per minute at the bottleneck machine, which is 70 W, 60 X, 47 Y, and 30 Z. This is option C.

Table 5.3 King Supply Makes Four Different Types of Plumbing Fixtures: W