Question

PARTI A vendor at a local baseball stadium must decide what course of action to take, sell ice cream or soft drinks at today's game. Each soft drink costs $0.25 and is sold for $1.25 while each ice cream costs $0.45 and is sold for $2.45. If the weather is warm she forecasts demand of 200 drinks or 150 ice creams but if the weather is cold, she forecasts demand of 150 soft drinks or 45 ice creams. a. Compute the payoffs for each level of demand for warm and cold weather b. Construct a payoff table, indicating the events and alternative courses of action c. Construct an opportunity loss table. d. Construct a decision tree. Based on her past experience at this time of year, the vendor estimates the probability of warm weather as 0.60. e. Determine the optimal action based on the maximax criterion. f. Determine the optimal action based on the maximin criterion. g. Compute the expected monetary value (EMV) for action soft drinks and action ice cream. h. Compute the expected opportunity loss (EOL) for action soft drinks and action ice cream. i. Explain the meaning of the expected value of perfect information (EVPI) in this problem. j. Based on the results of (g) or (h), which action would you chose? Why? k. Compute the coefficient of variation for each action. 1. Compute the return to risk ratio (RTRR) for each action. m. Based on (k) and (1) above, what action would you choose? Why? n. Compare the results of (1) and (m) and explain any differences.

Answer 1

You have asked multiple sub parts in the same question. I will address the first four parts. Please post the balance sub parts separately.

Profit per unit from soft drinks = sale price - cost price = $ 1.25 - 0.25 = $ 1.00 per unit

Profit per unit from ice cream = sale price - cost price = $ 2.45 - 0.45 = $ 2.00 per unit

Part (a)

Warm weather

Payoff from sale of soft drinks = 1.00 x 200 = $ 200

Payoff from sale of ice cream = $ 2.00 x 150 = $ 300

Cold weather

Payoff from sale of soft drinks = 1.00 x 150 = $ 150

Payoff from sale of ice cream = $ 2.00 x 45 = $ 90

Part (b)

Payoff table:

	ACTION
EVENT	Sell Soft Drinks	Sell Ice Cream
Cold weather	150	90
Warm Weather	200	300

Part (c)

Opportunity loss table:

	ACTION
EVENT	Sell Soft Drinks	Sell Ice Cream
Cold weather	150 - 150 = 0	150 - 90 = 60
Warm Weather	300 - 200 = 100	300 - 300 = 0

Maximum payoff possible in cold weather = max (150, 90) = 150

Maximum payoff possible in warm weather = max (200, 300) = 300

Part (d)

Decision tree:

Cold weather Profit $ 150 Sell Soft Drinks Warm weather Profit $ 200 Cold weather Profit $ 90 Sell Ice cream Warm weather Profit $ 300