Exam 19: Decision Theory

A silk screen T-shirt Company buys T-shirts and places designs on them.The cost of the T-shirt is $2.00.Placing the designs on shirts costs $3.00.The shirts sell for $12.Unsold shirts are donated to charity.The monthly demand for T-shirts with designs runs at a mean of 400 and a standard deviation of 50 T-shirts and is approximately normally distributed.What is the profit maximizing number of T-shirts to purchase each month? ____________________ T-shirts

Incremental analysis is a technique especially useful for inventory decisions.

In using the minimax regret criterion,we must first construct a regret table.

When Jessica takes the direct route to work,she gets there in 25 minutes if no train is at the railroad crossing.When a train is using the crossing,her travel time is 10 minutes longer.Her alternative is a route that takes 32 minutes to travel,but has no traffic signals or other delays.Assuming that shorter transit times are more desirable,which route will Jessica select if she uses the maximax criterion? Explain.

Tee shirts Tee Shirts Unlimited is providing shirts for an upcoming sports tournament.They assume demand will be either 2000,3000,4000,or 5000 shirts and they need to decide whether to produce 2000,3000,4000,or 5000 shirts.The payoff for each production/demand combination is shown in the table below. PAYOFFE Demand Altematives \ 10,000 \ 10,000 \ 10,000 \ 10,000 \ \ 15,000 \ 15,000 \ 15,000 -\ 4,000 \ \ 20,000 \ 20,000 -\ 11,000 \ 1,000 \ 13,000 \ 25,000 -The probabilities for demand levels 2000,3000,4000,and 5000 have been estimated to be 20%,40%,15%,and 25% respectively.Which production level provides the largest expected payoff?

Canoe rentals John's Canoe Rentals leases canoes each day from a supplier and rents them to customers who use them to float down the Delaware River.Each day,John can lease 10,20,or 30 canoes from his supplier.John assumes daily demand will be either 10,20,or 30 canoes.The payoff table for each lease/demand combination is shown below. PAYoFFE Demand Altemitives \ 140 \ 140 \ 140 -\ 20 \ 280 \ 280 30 -\ 180 \ 120 \ 420 -John assumes the probabilities for demand levels of 10,20,and 30 canoes is 40%,25%,and 35% respectively.What is the expected value of perfect information?

A new car salesman is being paid a straight salary,but has the choice to (a)continue with straight salary,(b)change to straight commission,or (c)change to a combination that includes a lower base salary and a commission on each sale of a new car.What states of nature might be useful in constructing a payoff table for this situation?

Why should we bother determining the expected value of perfect information when such information is practically never available?

When Jessica takes the direct route to work,she gets there in 25 minutes if no train is at the railroad crossing.When a train is using the crossing,her travel time is 10 minutes longer.Her alternative is a route that takes 32 minutes to travel,but has no traffic signals or other delays.Assuming that shorter transit times are more desirable,which route will Jessica select if she uses the maximin criterion? Explain.

A person builds a storm cellar in a region struck consistently with tornadoes.Which of the following decision making criteria does this typify?

A fruit stand manager must decide how many pounds of bananas to stock weekly.From past records it appears that the demand for bananas is approximately normal with a mean of 1,200 pounds and a standard deviation of 400 pounds.The cost of the bananas is $0.15 per pound and the usual selling price is $0.45 per pound.At the end of each week a hog farmer comes by the fruit stand and purchases any unsold,over-ripened bananas for $0.05 per pound.Calculate the amount of bananas the manager needs to purchase each week to maximize his profit. ____________________ pounds

Canoe rentals John's Canoe Rentals leases canoes each day from a supplier and rents them to customers who use them to float down the Delaware River.Each day,John can lease 10,20,or 30 canoes from his supplier.John assumes daily demand will be either 10,20,or 30 canoes.The payoff table for each lease/demand combination is shown below. PAYoFFE Demand Altemitives \ 140 \ 140 \ 140 -\ 20 \ 280 \ 280 30 -\ 180 \ 120 \ 420 -How many canoes should be leased using the minimax regret criterion?

Economy An investor has constructed the following payoff table for his profit in thousands of dollars. The state of the economy will be Invest in company Weak Moderate Strong -\ 45 \ 35 \ 65 -\ 25 \ 25 \ 50 \ 29 \ 33 \ 35 -Determine the expected opportunity loss (EOL)from investing in each company. Company A: ____________________ thousand Company B: ____________________ thousand Company C: ____________________ thousand

For each of the following,indicate whether the behavior represents the maximin criterion or the maximax criterion.Explain your reasoning. A)A truck driver is behind schedule and knows he is approaching an area where police radar is often encountered, but he continues driving at 20 mph over the speed limit. Explain: B)A struggling retailer hires a public relations firm to carry out an intensive promotional campaign for her store. If the campaign is not extremely successful, the retailer will not be able to pay the PR firm and will be in danger of defaulting on next month's payroll. Explain: C)The owner of a medical clinic buys liability insurance. Explain:

A civic organization cooks and serves pancakes once a year as a fundraiser and has done so for the past 25 years.The pancake grill size requires pancakes to be cooked in advance of the orders for them.All labor is donated,but the electricity and pancake supplies cost $0.20 per pancake.Each pancake sells for $0.60.From past records it appears that the distribution of pancake sales is approximately normal with a mean of 3000 and a standard deviation of 450.Cooked,but unsold pancakes are given to anyone who wishes to take them.Find the number of cooked pancakes that will yield the maximum profit for the project. ____________________ pancakes Remove all commas from your answer before submitting.

The profit if one more unit is stocked and sold is known as marginal profit.

Regrets refer to the differences between each payoff and the worst possible payoff if that state of nature were to occur.

The minimax regret criterion specifies selection of the alternative with the lowest maximum regret.

Canoe rentals John's Canoe Rentals leases canoes each day from a supplier and rents them to customers who use them to float down the Delaware River.Each day,John can lease 10,20,or 30 canoes from his supplier.John assumes daily demand will be either 10,20,or 30 canoes.The payoff table for each lease/demand combination is shown below. PAYoFFE Demand Altemitives \ 140 \ 140 \ 140 -\ 20 \ 280 \ 280 30 -\ 180 \ 120 \ 420 -John assumes the probabilities for demand levels of 10,20,and 30 canoes is 40%,25%,and 35% respectively.Which leasing alternative will provide the largest expected payoff?

State of Nature The following table displays the payoffs (in thousands of dollars)for five different decision alternatives under three possible states of nature: State of Nature Alternative I Prob. = II Prob. = III Prob. = A \ 110 \ 80 -\ 20 B \ 90 \ 85 \ 10 C \ 45 \ 65 \ 45 D \ 30 \ 60 \ 65 E \ 10 \ 25 \ 70 -Calculate the expected opportunity loss for Alternative A (in thousands of dollars). ____________________ thousand