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# How Much To Order

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The steak and Chop Butcher Shop purchase steak from a local meatpacking house. The meat is purchased on Monday at \$2.00 per pound, and the shop sells the steak for \$3.00 per pound. Any steak left over at the end of the week is sold to a local zoo for \$.50 per pound. The possible demands for steak and the probability of each are shown in the following table:

Demand (lb.) Probability
20 .10
21 .20
22 .30
23 .30
24 .10
1.00

The shop must decide how much steak to order in a week. Construct a payoff table for this decision situation and determine the amount of steak that should be ordered, using expected value.

#### Solution Preview

The steak and Chop Butcher Shop purchase steak from a local meatpacking house. The meat is purchased on Monday at \$2.00 per pound, and the shop sells the steak for \$3.00 per pound. Any steak left over at the end of the week is sold to a local zoo for \$.50 per pound. The possible demands for steak and the probability of each are shown in the following table:

Demand (lb.) Probability
20 0.1
21 0.2
22 0.3
23 0.3
24 0.1
1

The shop must decide how much steak to order in a week. Construct a payoff table for this decision situation and determine the amount of steak that should be ordered, using expected value.

Demand (lb.) Probability
20 0.1
21 0.2
22 0.3
23 0.3
24 0.1
1
Purchase price= \$2.00 per pound
Selling price for steak sold = \$3.00 per pound
Price at which unsold steak is sold to the zoo= \$0.50 per pound

Case I: Quantity ordered= 20 pounds

Purchase Amount= \$40.00 =20 x \$2.

Demand (lb.) Probability Quantity sold Revenue for sold steak Quantity Unsold (Purchase - Demand) Revenue for steak sold to the zoo Expected ...

#### Solution Summary

The solution arrives at a decision on how much steak to order by calculating a payoff table for each decision and arriving at the optimal decision.

\$2.19