Question

Sally's Silk Screening produces specialty T-shirts that are primarily sold at special events. She is trying to decide how many to produce for an upcoming event. During the event itself, which lasts one day, Sally can sell T-shirts for $20 a piece. However, when the event ends, any unsold T-shirts are sold for $4 a piece. It costs Sally $8 to make a specialty T-shirt. Using Sally's estimate of demand that follows, how many T-shirts should she produce for the upcoming event? ______T-shirts. (input an integer,e.g. 100)

demand probability
300 0.05
400 0.10
500 0.40
600 0.30
700 0.10
800 0.05

Answer 1

To determine how many T-shirts Sally should produce for the upcoming event, calculate the expected profit for each possible quantity and choose the one that maximizes profit.

Step-by-step explanation:

To determine how many T-shirts Sally should produce for the upcoming event, we need to calculate the expected profit for each possible quantity. The expected profit is calculated by multiplying the demand probability for each quantity by the profit made for that quantity.

For example, if Sally produces 300 T-shirts and the demand probability is 0.05, the expected profit for that quantity is:

(0.05 * (300 * ($20 - $8))) + ((1 - 0.05) * (300 * ($4 - $8))).

By calculating the expected profit for each quantity, Sally can determine the quantity that maximizes her profit.