An electronics manufacturer has outsourced production of its latest media players to a contract manufacturer in Asia. Demand for the players has exceeded all expectations, whereas the contract manufacturer has limited production capacity. The electronics manufacturer sells three types of players—a 40-GB player, a 20-GB player, and a 6-GB player. For the upcoming holiday season, the demand forecast for the 40-GB player is normally distributed, with a mean of 20,000 and a standard deviation of 7,000, the demand forecast for the 20-GB player has a mean of 40,000 and a standard deviation of 11,000, and the demand forecast for the 6-GB player has a mean of 80,000 and a standard deviation of 16,000. The 40-GB player has a sale price of $200, a production cost of $100, and a salvage value of $80. The 20-GB player has a sale price of $150, a production cost of $90, and a salvage value of $70. The 6-GB player has a sale price of $100, a production cost of $70, and a salvage value of $50.
a. How many units of each type of player should the electronics manufacturer order if there are no capacity constraints?
b. The contract manufacturer has available production capacity of only 140,000 units. What is the expected profit if the electronics manufacturer orders 20,000 units of the 40-GB player, 40,000 units of the 20-GB player, and 80,000 units of the 6-GB player?
c. How many units of each type of player should the electronics manufacturer order if the available capacity is 140,000? What is the expected profit?