Question 3 Solar Heat Inc is a supplier of heaters to households. The company is

Question

Question 3 Solar Heat Inc is a supplier of heaters to households. The company is considering whether to provide a solar heating installation service to its customers. The management of the company has determined that a startup cost of $150,000 would be necessary in order to get a unit profit of $2,000 for each solar heating system installed. The following estimates of the probability of various demand levels have been obtained from the historical information. Number of solar heating systems installed 50 100 200 300 Probability 0.25 0.35 0.30 0.10 a. Construct the payoff table indicating the events and alternative courses of action. [2 marks] heating installation service. [5 marksl c. Calculate the expected value of perfect information. [3 marks]

Explanation / Answer

a. The payoff table is

b.

Expected opportunity of loss = 500000 * 0.25 + 400000 * 0.35 + 200000 * 0.30 + 0 * 0.10 = 325000

c.

Expected value without perfect information = -50000 * 0.25 + 50000 * 0.35 + 250000 * 0.30 + 450000 * 0.10 = 125000

If we have the information of the demand, based on course of action in part (a), we will not provide installation service when the demand is of 50 solar heating systems else provide.

Expected value with perfect information = 0 * 0.25 + 50000 * 0.35 + 250000 * 0.30 + 450000 * 0.10 = 137500

So, Expected value of perfect information =  Expected value with perfect information - Expected value without perfect information = 137500 - 125000 = 12500

Number of solar heating systems Probability Payoff Course of Action Oppportunity loss = Best Payoff - Payoff Received 50 0.25 50*2000-150000 = -50000 No 500000 100 0.35 100*2000-150000 = 50000 Yes 400000 200 0.30 200*2000-150000 =250000 Yes 200000 300 0.10 300*2000-150000 =450000 Yes 0

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