MGNT 4640
1.
DECISION ANALYSIS HOMEWORK #2
The following payoff table provides the profits for each of four alternatives in
each of three states of nature:
States of Nature
Alternatives
A
B
C
1
120
60
-20
2
90
80
100
3
81
81
81
4
-50
90
110
___________________________________
The probabilities for the states of nature are:
P(A)=0.8, P(B) = 0.1, and P(C) = 0.1.
(a)
(b)
(c)
(d)
2.
What decision would be made based on the optimistic criterion?
What decision would be made based on the conservative criterion?
What decision would be made based on the expected value criterion?
Develop a regret table and use the regret criterion to find the decision.
Teresa Granger is the manager of Chicago Cheese, which produces cheese
spreads including E-Z Spread Cheese. The probability of various sales levels, in
cases, is as follows:
Sales in Cases
10
11
12
13
14
Probability
0.2
0.3
0.2
0.2
0.1
A case of E-Z Spread Cheese sells for $100 and has a cost of $75. Any cheese
that is not sold by the end of the week is sold to a local food processor for $50.
How many cases of E-Z Spread Cheese should Teresa produce each week to
maximize profit? Use Expected Net Marginal Profit Analysis to answer this
question.
3. During Christmas, Harry’s Hardware sells Christmas trees for a substantial profit.
Unfortunately, any trees not sold at the end of the season are worthless. The table
on the next page shows the demand for Christmas trees.
MGNT 4640
DECISION ANALYSIS HOMEWORK #2
DEMAND FOR CHRISTMAS TREES
PAGE 2
PROBABILITY
50
75
100
125
150
175
200
0.05
0.10
0.20
0.30
0.20
0.10
0.05
Harry sells trees for $15 each, but his cost is only $6. Solve each part below, first
by using E(NMP) analysis. Then solve again, using pc.
(a)
(b)
(c)
How many trees should Harry stock at his hardware store?
If the cost increased to $12 per tree and Harry continues to sell trees for $15
each, how many trees should Harry stock?
Harry is thinking about increasing the price to $18 per tree. Assume that the
cost per tree is $6. It is expected that the probability of selling 50, 75, 100,
or 125 trees will be 0.25 each. Harry does not expect to sell more than 125
trees with this price increase. What supply level do you recommend?
4.
In addition to selling Christmas trees during the Christmas holidays, Harry’s
Hardware sells all of the ordinary hardware items. One of the most popular items
is Great Glue HH, a glue made for Harry’s Hardware. The selling price is $2 per
bottle, but unfortunately, the glue gets hard and unusable after one month. The
cost of the glue is 75 cents. During the past several months, the mean sales of
glue was 60 units, and the standard deviation was 7. How many bottles of glue
should Harry’s Hardware stock? Assume that sales follow a normal distribution.
5.
The marginal profit on Washington Reds, a brand of apples from the state of
Washington, is $15 per case. The marginal loss is $35 per case. During the past
year, the mean sales of Washington Reds was 45,000 cases, and the standard
deviation was 4,450. How many cases of Washington Reds should be brought to
market? Assume that sales follow a normal distribution.
Answers
1.
(a) Alternative 1; 120 (b) Alternative 3; 81 (c) Alternative 1;
expected value = 100 (d) Alternative 2; least maximum regret = 30
2.
Supply 12 cases
4.
pc = .375; supply 62 bottles
3. (a) Supply 125 trees
(b) Supply 100
(c) Supply 100
5. pc = .70; supply 42,686 cases