A buyer for a large sporting goods store chain must place orders for professional footballs with the football manufacturer six months prior to the time the footballs will be sold in the stores. The buyer must decide in November how many footballs to order for sale during the upcoming late summer and fall months. Assume that each football costs the chain $45. Furthermore, assume that each can be sold for a retail price of $90. If the footballs are still on the shelves after next Christmas, they can be discounted and sold for $35 each. The probability distribution of consumer demand for these footballs (in hundreds) during the upcoming season has been assessed by the market research specialists and is presented below. Finally, assume that the sporting goods store chain must purchase the footballs in lots of 100 units. Demand (in hundreds) Probability 4 0.30 5 0.50 6 0.20 a) Construct a decision tree to identify the buyer’s course of action that maximizes the expected profit earned by the chain from the purchase and subsequent sale of footballs in the coming year. b) What is the optimal strategy for order quantity, and what is the expected profit in that case?
A buyer for a large sporting goods store chain must place orders for professional footballs with the football manufacturer six months prior to the time the footballs will be sold in the stores. The buyer must decide in November how many footballs to order for sale during the upcoming late summer and fall months. Assume that each football costs the chain $45. Furthermore, assume that each can be sold for a retail price of $90. If the footballs are still on the shelves after next Christmas, they can be discounted and sold for $35 each. The probability distribution of consumer demand for these footballs (in hundreds) during the upcoming season has been assessed by the
| Demand (in hundreds) | Probability |
| 4 | 0.30 |
| 5 | 0.50 |
| 6 | 0.20 |
a) Construct a decision tree to identify the buyer’s course of action that maximizes the expected profit earned by the chain from the purchase and subsequent sale of footballs in the coming year.
b) What is the optimal strategy for order quantity, and what is the expected profit in that case?
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