Question

The owner of a clothing score must decide how many men's shirt to order for the new season. For a particular type of shirt, she must order in quantities of 100 shirts. If she orders 100 shirts, her cost is $10 per shirt, if she orders $200, her cost is $9 per shirt; and is she orders 300 or more shirts, her cost is $8.50 per shirt. her selling price for the shirt is $12, but any shirts that remain unsold at the end of the season are sold at her famous "half-price, end-of-season sale." For the sake of simplicity, she is willing to assume that the demand for this type of shirt will be 100, 150, 200, 250 shirts. Of course , she cannot sell more shirts than she stocks.she is also willing to assume that she will suffer no loss of goodwill among her customers if she understocks and the customers cannot buy all the shirts they want. Furthermore, she must place her order today for the entire season; she cannot wait to see how the demand is
running for this type of shirt. Construct a payoff table to help the owner decide how many shirts to order.

Answer 1

The attached shows the profit in dollars for different combinations of orders (bought) and sales (sold). We assume that every left-over shirt is sold at half price ($6).

The number that goes in each cell of the table is ...

... profit = ($12 - cost per shirt)×(number sold) - (cost per shirt - $6)×(number unsold)

where ...

... "number sold" = min(number ordered, demand)

... "number unsold" = number ordered - number sold

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Comment on the table

Based on this table, I'd be inclined to order 200 shirts, as the profit is highest for all but the greatest and least demand, and there is never an actual loss. Of course, an order of 100 shirts guarantees a profit, so that may be preferred under some circumstances.