Question

The produce manager at the local grocery store must determine how many pounds of bananas to order weekly. Based upon past experience, the demand for bananas is expected to be 100, 150, 200, or 250 pounds with the following probabilities: 100lbs 0.20; 150lbs 0.25, 200lbs 0.35, 250lbs 0.20. The bananas cost the store $.45 per pound and are sold for $.85 per pound. Any unsold bananas at the end of each week are sold to a local zoo for $.30 per pound.

Use your knowledge of decision analysis to model and solve this problem in order to recommend how many pounds of bananas the manager should order each week

please use excel spreadsheets for the answers! thank you!

Answer 1

The solution is based on EMV criterion of Decision Making, where-in for each decision option, the pay-offs under various States of Nature (SON’s) are multiplied by the respective probability to obtain the EMV for that decision option. Then, the decision option which yields the maximum EMV is selected.

Purchase Cost,PC	0.45
Sale Price, SP	0.85
Discounted Sale Pric, DP	0.3

If	Then
D≤Q	SP*D + (Q-D)*DP - PC*Q
D>Q	(SP-PC)*D

	Pay-off	EMV
Q	D
100	150	200	250	How did we calculate EMV
100	40.0	40.0	40.0	40.0	40.00
150	32.5	60.0	60.0	60.0	54.50	= (32.5*0.2)+(60*0.25)+(60*0.35)+(60*0.2)
200	25.0	52.5	80.0	80.0	62.13
250	17.5	45.0	72.5	100.0	60.13
P(D)	0.20	0.25	0.35	0.20

Since EMV is maximum at $62.3 for Q = 200,

Optimum order quantity is 200 pounds of bananas per week.

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