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 $15 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:

Note that it can be calculated that the mean demand is 13,600. Please show all your work, otherwise you will get no points for your answers.

(e) If both parties agree on a revenue-sharing contract, in which the wholesale price is reduced to $30, and Target would give the manufacturing company 20% of its revenue for all costumes sold, what is the expected profit of the manufacturing company in such a deal?