You have been asked to put together a capacity plan for a critical bottleneck operation at the Surefoot Sandal Company. Your capacity measure is number of machines. Three products (men's women's, and kid's sandals) are manufactured. The time standards (processing and setup), lot sizes, and demand forecasts are given in the following table. The firm operates two 8- hour shifts, 5 days per week, 50 weeks per year. Experience shows that a capacity cushion of 5 percent is sufficient. Time Standards Demand Forecast Processing Setup Lot Size (pairs/xx) Product (hr/pair) (hr/lot) (pairs/lot) Men's sandals 0.05 0.5 240 80,000 Women's sandals 0.10 2.2 180 60,000 Kid's sandals 0.02 3.8 360 120,000 a. How many machines are needed at the bottleneck? b. If the operation currently has two machines, what is the capacity gap? c. If the operation can not buy any more machines, which products can be made? Men's sandals contribute $2/pair as profit, Women's sandals contribute $4/pair and Kid's sandals contribute $1.75/pair as profit. What can be the maximum profit generated in this situation. d. If the operation currently has five machines, what is the utilization