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 and 2000 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

If we assumes we setup machine for product A x times, and B y times, the total hours required is 0.5*3000 + 0.8*2000 + 2*x + 8 * y = 3100+2x+8y. Notice that due to the capacity restriction x has to be no smaller than 150 hours (3000/20) and y has to be no smaller than 50 hours (2000/40). so total required hours must exceed 3100+2*150+8*50=3800. The management prefer a 15% capacity cushion, which means the total duration prepared for the processing should be at least 3800 * (1+15%) = 4370 hours.

If one machine operates eight hours per day, five days per week and 50 weeks a year, it operates 5*8*50 = 2000 hours in total.

That's why we need 2 more machines (3 machines in total since 4370 > 2*2000).