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 pair 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) What is the payoff if the store orders 400 footballs and quantity demanded is 400 footballs?
(B) What is the payoff if the store orders 400 footballs and quantity demanded is 500 footballs?
(C) What is the payoff if the store orders 400 footballs and quantity demanded is 600 footballs?
?(D) What is the payoff if the store orders 500 footballs and quantity demanded is 400 footballs?
?(E) What is the payoff if the store orders 500 footballs and quantity demanded is 500 footballs?
?(F) What is the payoff if the store orders 500 footballs and quantity demanded is 600 footballs?
?(G) What is the payoff if the store orders 600 footballs and quantity demanded is 400 footballs?
?(H) What is the payoff if the store orders 600 footballs and quantity demanded is 500 footballs?
?(I) What is the payoff if the store orders 600 footballs and quantity demanded is 600 footballs?
What will be an ideal response?
Payoff table
| D = 400 | D = 500 | D = 600 | |
| Order 400 | $18,000 | 18,000 | 18,000 |
| Order 500 | $17,000 | $22,500 | $22,500 |
| Order 600 | $16,000 | $24,500 | $27,000 |
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