The single milling machine at Stout Manufacturing was severely overloaded last year. The plant operates eight hours per day, five days per week, and 50 weeks per year. Management prefers a capacity cushion of 15 percent.

Two major types of products are routed through the milling machine:

- The annual demand for product A is 3000 units, with a batch size of 20 units. The standard processing time for A is 0.5 hours/unit, and the standard setup time is 2 hours.
- The annual demand for product B is 2000 units, with a batch size of 40 units. The standard processing time for B is 0.8 hours/unit, and the standard setup time is 8 hours.

How many new milling machines are required if Stout does not resort to any short-term capacity options?

A. No new machines
B. 1 or 2 new machines
C. 3 or 4 new machines
D. More than 4 new machines

The calculation for the number of new milling machines required at Stout Manufacturing is essentially a capacity planning problem. We first need to calculate the total processing time for both products. For product A, this is 3000 units * 0.5 hours/unit = 1500 hours, and for product B it is 2000 units * 0.8 hours/unit = 1600 hours.

The total time then is 3100 hours, which includes the processing time. Adding setup times, we get 150 hours for A (3000 units/20 units/batch * 2 hours/setup) and 400 hours for B (2000 units/40 units/batch * 8 hours/setup), totaling to 550 hours. Consequently, the total time, including processing and setup, is 3650 hours

Next, we need to consider the capacity cushion. Management wants a capacity cushion of 15 percent, so the total time needs to be divided by (1 - 0.15) = 0.85, giving us a total of 4294 hours. The plant operates eight hours a day, five days a week, and 50 weeks a year, so the total available time is 8 hours/day * 5 days/week * 50 weeks/year = 2000 hours/year. Consequently, Stout Manufacturing would need 4294/2000 = 2.147, in other words, 3 new machines to meet demand without resorting to short-term capacity solutions.

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