Question

A company which manufactures and sells​ T-shirts for sporting​ events is providing shirts for an upcoming tournament. Each shirt will cost ​$6 to produce and will be sold for ​$12. Any unsold shirts at the end of the tournament can be sold for ​$5 apiece in the near future. The company assumes the demand for the shirts will be 2,500​, 5,000​, 7,500​, or 10, 000. The company also estimates that the probabilities of each of these sales levels occurring will be 15%, 20​%, 30​%, and 35​%, respectively. Determine the expected monetary value of the project if the company chooses to print 7,500 shirts for the tournament. The expected monetary value is​ $_______

Answer 1

When company chose to print 7500 shirts:

Payoff when demand is 2500 = 2500(12-6) + 5000( 5 - 6)

= 15000 - 5000

= $10000

Payoff when demand is 5000 = 5000(12-6) + 2500( 5 - 6)

=30000 - 2500 = $ 27,500

Payoff when demand is 7500 = 7500(12-6) = $45,000

Payoff when demand is 10,000 = 7500(12-6) + 2500(0)= $45000

Hence, Expected monetary value = (10,000)15% +(27,500) 20% + (45000) 30% + (45,000)*35%

Expected monetary value = 1500 + 5500 + 13,500 + 15750

= $36,250

So, Expected monetary value when company chose to print 7500 shirts is $ 36,250