Question

The decision maker in a supermarket must decide how many boxes of bananas to order. The bananas come in boxes of 100 lbs, 500 lbs, and 1,000 lbs, and the decision maker has determined to order exactly one of the three types of boxes. Naturally, there is a quantity discount: each pound of bananas in the regular box costs 20¢, in the big box the price is 15¢ per pound, & in the huge box it is 12¢ per pound. Demand has been estimated to be either 50 lbs, 250 lbs, 700 lbs, or 900 lbs with probabilities of 0.3, 0.4, 0.2, and 0.1, respectively. Bananas sell for 40¢ per pound, and customer demand must be satisfied. In case the store does not have sufficient supplies, they must purchase them from one of their competitors for 60¢ per pound. Leftover bananas have a salvage value of 5¢ per pound. Which of the boxes should be ordered and what is the expected profit? Show all relevant computations.

Answer 1

To determine the expected profit for ordering bananas, we calculate the profit or loss for each demand scenario considering purchase and selling prices, additional costs for unsupplied demand, and salvage values. We then weigh the results by their probabilities to decide on the most profitable box size to order.

Step-by-step explanation:

The supermarket decision maker is tasked with choosing the most profitable box size of bananas to order considering various demand scenarios, costs, and salvage values. To determine the expected profit for each box size, we need to calculate the profit or loss for every demand scenario, considering the cost price and selling price of the bananas, the extra cost to fulfill unsatisfied demand, and the salvage value of leftover bananas. We then multiply these profits or losses by their respective probabilities to obtain the expected profits for all three box sizes.

• The regular box has 100 lbs and costs 20¢/lb.
• The big box has 500 lbs and costs 15¢/lb.
• The huge box has 1,000 lbs and costs 12¢/lb.

Given the probabilities and demand estimates, and the fixed selling price of 40¢/lb and salvage value of 5¢/lb for excess bananas, these computations allow the decision maker to select the box that maximizes expected profit. The calculations for each scenario entail subtracting the cost of the box, adding the revenue from sales, and including the cost of purchasing additional bananas or the salvage value of excess, depending on demand met.