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# Linear programming

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5) The owner of The East End Technology Company has collected statistics on previous demand:

Daily Demand 0 10 20 30 40 or more
# of days 5 8 15 12 10

a. Using the expected monetary value model, what is the best development alternative?
b. What is the value of perfect information?
c. Draw the decision tree for this problem.
d. Using the maximum likelihood criteria, determine the best alternative.

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The solution provides answers to questions on decision trees and value of perfect information.

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5. The owner of The East End Technology Company has collected statistics on previous de­mand:

Daily Demand 0 10 20 30 40 or more
# of days 5 8 15 12 10

a. Using the expected monetary value model, what is the best development al­ter­na­tive?
b. What is the value of perfect information?
c. Draw the decision tree for this problem.
d. Using the maximum likelihood criteria, determine the best alternative.

First calculate the probability of each number being sold

Daily Demand # of days Probability
0 5 0.1 =5/50
10 8 0.16 =8/50 and so on
20 15 0.3
30 12 0.24
40 or more 10 0.2
50 1

Conditional Profit Table
Possible Demand (Sales) Possible Stock action
0 10 20 30 40
0 0.00 (7.50) (15.00) (22.50) (30.00)
10 0.00 15.00 7.50 0.00 (7.50)
20 0.00 15.00 30.00 22.50 15.00
30 0.00 15.00 30.00 45.00 37.50
40 0.00 15.00 30.00 45.00 60.00

a. Using the expected monetary value model, what is the best development al­ter­na­tive?

Expected profit from stocking 0

Demand Probability Conditional Profit Expected Profit=Conditional profit X Prob

0 0.1 \$0.00 \$0.00
10 0.16 \$0.00 \$0.00
20 0.3 \$0.00 \$0.00
30 0.24 \$0.00 \$0.00 ...

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