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In: Statistics and Probability

A machine shop owner is attempting to decide whether to purchase a new drill press, a...

A machine shop owner is attempting to decide whether to purchase a new drill press, a lathe, or a grinder.  The profit or loss from each purchase are shown in the following table where one of two states of nature could occur (the company succeeds in getting a military contract, or it does not get a contract).

 
Contract status
 
Purchase
Get Contract
No contract
Drill press
40000
-8000
Lathe
25000
4000
Grinder
12000
10,000

 

a-for each purchase decision show the numbers you use when using an optimistic method of choosing which one item to purchase and indicate which item is purchased by this method.

b-for each purchase decision show the numbers you use when using a conservative method of choosing which one item to purchase and indicate which item is purchased by this method.

c-show the numbers you use in a new table using the minimax regret method of choosing which one item to purchase and indicate which item is purchased by this method.

d-What is the expected monetary value of each purchase option when the probability of getting contract is .4 and which is the best option under this probability?

e-Since .4 may be incorrect as the probability of getting a military contract, over what range of values for the probability of getting a contract would each purchase option be the most favored? Show your work!

Solutions

Expert Solution

Under the maximax criteria, the best decision for the machine shop owner is to purchase a new drill press as it has the highest payoff. The payoff is $40,000

Under the maxmin criteria, the best decision for the machine shop owner is to purchase a new grinder press as it has the highest payoff. The Payoff = $6,000

According to minimax regret, we compute total regrets for each alternative and select the one with the smallest total regret. In this case, the machine shop owner chooses to buy grinder.Payoff = $26,000

Hurwicz’s criterion = α(maximum payoff for an alternative) + (1-α)(minimum payoff for an alternative)

The option that should be selected according to Hurwicz decision maker when α = 0.4 is that shop owner should purchase drill. The payoff is $13,600

orchestra answered 2 years ago
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