A costume manufacturing company produces kids' costumes. It has a new design for the upcoming Halloween and sells it to Target at a wholesale price of $40.The production cost of the costume is$20 for the company. Target sells the costume at a retail price of $80. If any unsold costumes, Target will ship them to an outlet store to sell them next year, but at a discount price of $40. But this incurs an additional $30 shipping and inventory holding cost for each costume. The demand of Target is estimated to be

Demand Probability

Cumlative probability

10000 10% 10%

12000 30% 40%

15000 30% 70%

16000 30% 100%

Note that it can be calculated that the mean demand

is13,900.

(a)How many costumes should Target order for the season?

(b)On average, how many costumes will be shipped to an

outlet store?

(c)What is the expected profit for Target? What is the

profit for the manufacturing company?

(d) If the supply chain were coordinated (i.e., centralized),

what would the optimal order quantity be? What would the total supply chain

profit be?

(e)Keeping the $40 wholesale price, the manufacturing

company proposes a buy-back contract with a buy-back price$25. The

manufacturing company also sells unsold costumes in an outlet store at a

discount price of $40, by incurring a $30 shipping and holding cost. How many

costumes should Target order for the season? What is the expected profit for

Target? What is the profit for the manufacturing company?

(f)If both parties agree on a revenue-sharing contract, in

which the wholesale price is reduced to $30, and Target would give the

manufacturing company20%of its revenue for all costumes sold, what

is the expected profit of the manufacturing company in such a deal?