A ski jacket manufacturer has outsourced production to a supplier in Asia. The electronics manufacturer sells three types of jackets—a high end, a mid-range, and a low end jacket. For the upcoming winter season, the demand forecast for the high end jacket is normally distributed, with a mean of 600 and a standard deviation of 400, the demand forecast for the mid-range jacket has a mean of 1,000 and a standard deviation of 500, and the demand forecast for the low-end jacket has a mean of 2,000 and a standard deviation of 600. The high end jacket has a sale price of $300, a production cost of $120, and a salvage value of $100. The mid-range jacket has a sale price of $200, a production cost of $100, and a salvage value of $85. The low end jacket has a sale price of $110, a production cost of $70, and a salvage value of $50.
a. How many jackets of each type should the manufacturer order if there are no capacity constraints?
b. The supplier has available production capacity of only 3,600 jackets. What is the expected profit if the manufacturer orders 600 high end jackets, 1,000 mid-range jackets, and 2,000 low end jackets?
c. How many jackets of each type should the manufacturer order if the available capacity is 3,600? What is the expected profit?