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 3,000 units and 2,000 units for product B. The batch size for A is 20 units and 40 units for B. The standard processing time for A is 0.5 hours/unit and 0.8 hours/unit for B. The standard setup time for product A is 2 hours and 8 hours for product B. 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

Question

Quizplus · Accepted Answer

First, calculate the total hours required for both products A and B, including setup and processing time. For product A: Setup time = (3000 units / 20 units/batch) * 2 hours/setup = 300 hours Processing time = 3000 units * 0.5 hours/unit = 1500 hours Total for A = 1800 hours For product B: Setup time = (2000 units / 40 units/batch) * 8 hours/setup = 400 hours Processing time = 2000 units * 0.8 hours/unit = 1600 hours Total for B = 2000 hours Combined total = 3800 hours The plant operates 8 hours/day * 5 days/week * 50 weeks/year = 2000 hours/year. Considering a 15% capacity cushion, the effective capacity = 2000 * 0.85 = 1700 hours/machine/year. The total required hours (3800) divided by the effective capacity per machine (1700) gives approximately 2.24, indicating that Stout Manufacturing needs 1 or 2 new machines to meet the demand without resorting to short-term capacity options.

The Single Milling Machine at Stout Manufacturing Was Severely Overloaded