1) A television network earns an average of $1.6 million each season from a hit program and loses an average of $400,000 each season on a program that turns out to be a flop, and of all programs picked up by this network in recent years, 25% turn out to be hits and 75% turn out to be flops. a) Construct a decision tree to help the television network identify the strategy that maximizes its expected profit in responding to a newly proposed television program. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities. b) What should the network do? What is their expected profit? c) The network can conduct market research to determine whether a program will be a hit or a flop. If the market research report is perfectly reliable, what is the most the network should be willing to pay for it?
1) A television network earns an average of $1.6 million each season from a hit program and loses an average of $400,000 each season on a program that turns out to be a flop, and of all programs picked up by this network in recent years, 25% turn out to be hits and 75% turn out to be flops.
a) Construct a decision tree to help the television network identify the strategy that maximizes its
expected profit in responding to a newly proposed television program. Make sure to label all decision
and chance nodes and include appropriate costs, payoffs and probabilities.
b) What should the network do? What is their expected profit?
c) The network can conduct
2) 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?
Please explain how to create Decision Tree in Excel.
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