6. A small building contractor has recently experienced two successive years in
ID: 2948306 • Letter: 6
Question
6. A small building contractor has recently experienced two successive years in which work opportunities exceeded the firm's capacity. The contractor must now make a decision on capacity for next year. Estimated profits under each of the three possible states of nature are as shown in the table below. Which alternative should be selected if the decision criterion is
a) Maximax
b) Maximin
c) Equally likely (Laplace)?
The decision criterion when equally likely is Do Nothing $82,500
d) Minimax regret?
Suppose that the contractor is able to assess the probability of demand as P(Low) = 0.25, P(Medium) = 0.47, and P(High) = 0.28.
e) Determine the expected profit of each alternative. Which alternative is best? Why?
6. A small building contractor has recently experienced two successive years in which work opportunities exceeded the firm's capacity. The contractor must now make a decision on capacity for next year. Estimated profits under each of the three possible states of nature are as shown in the table below. Which alternative should be selected if the decision criterion is
a) Maximax
b) Maximin
c) Equally likely (Laplace)?
The decision criterion when equally likely is Do Nothing $82,500
d) Minimax regret?
Suppose that the contractor is able to assess the probability of demand as P(Low) = 0.25, P(Medium) = 0.47, and P(High) = 0.28.
e) Determine the expected profit of each alternative. Which alternative is best? Why?
Explanation / Answer
SINCE THE TABLE IS NOT GIVEN, SO I AM ASSUMING THE TABLE TO BE:-
Low Demand
High Demand
Do Nothing
$50,000
$60,000
Expand
$20,000
$80,000
Sub contract
$40,000
$70,000
(A) Maximax
The maximums of the rows are
Row 1
$60,000
Row 2
$80,000
Row 3
$70,000
The maximum of the row maximums is $80,000. It is corresponding to the decision Expand.
(B) Maximin
The minimums of the rows are
Row 1
$50,000
Row 2
$20,000
Row 3
$40,000
The maximum of the row minimums is $50,000. It is corresponding to the decision Do nothing
(C) Laplace
The expected values of the payoffs are(assuming equal probabilities to the two states of nature)
Row 1
0.5(50000)+0.5(60000)=55000
Row 2
0.5(20000)+0.5(80000)=50000
Row 3
0.5(40000)+0.5(70000)=55000
There are two choices Do nothing and Sub contract each with maximum expected payoff $55,000
(D). Minimax Regret
Prepare the regret table
Pay off table
Low Demand
High Demand
Do Nothing
$50,000
$60,000
Expand
$20,000
$80,000
Sub contract
$40,000
$70,000
Regret Table
Low Demand
High Demand
Do Nothing
$0
$20,000
Expand
$30,000
$0
Sub contract
$10,000
$10,000
Maximmum of the rows are
Row 1
$20,000
Row 2
$30,000
Row 3
$10,000
The minimum of the maximum regret is $10,000. It corresponds to the decision Sub contract
RESULTS:-
Decsion criterion
Best Decision
Maximax
Expand
Maximin
Do nothing
Laplace
Do nothing or Sub contract
Minimax Regret
Sub contract
Low Demand
High Demand
Do Nothing
$50,000
$60,000
Expand
$20,000
$80,000
Sub contract
$40,000
$70,000
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