Question

A city is hosting an annual marathon event and wants to produce t-shirts. Maria was able to obtain previous years’ demand and probability data as given in below table. She also estimates:

Selling price is $10, cost is $3, and the salvage value is $1.

Calculate all numbers in the payoff table. Show all work. How many shirts should be made to maximize profit?

	Demand = 1000, 20%	Demand = 2000, 30%	Demand = 3000, 30%	Demand = 4000, 20%	Profit
Make 1000
Make 2000
Make 3000
Make 4000

Answer 1

We complete the table as shown below:

Here, the calculation can be explained with an example. Suppose, the make quantity is 3000 and the Demand is 2000. The profit will be obtained on 2000 unit. Profit = 2000 * Overage cost = 2000 * 7 = 14000. There will be a loss of an excess quantity of 3000 - 2000 = 1000 units. Loss = 1000 * Underage cost = 1000 * 2 = 2000. Hence, net profit = 14000 - 2000 = $12,000. Similarly, if Make is 1000, Demand is 3000, the maximum quantity sold will be 1000. Profit = 1000 * 7 = 7000.

Hence, as seen from above, the maximum profit is for Make quantity = 3000 units

3000 shirts should be made.

----------------------------------------------------------------------------------------------------------------------------------------------------

In case of any doubt, please ask through the comment section before Upvote/downvote.