The Universal Uniforms store sells lab coats every year to medical students. The coats have to be ordered in September of the previous year and at that time, demand is uncertain. The coats are bought from a supplier at $4 a piece and sold in the store for $20 a piece. If by January, some coats are left unsold, they are sent to Goodwill by a firm that charges 50 cents per coat they have to take. If medical professionals come to the store wanting to buy an official coat but Universal Uniforms has run out, the store quickly makes an unofficial coat using a basic lab coat from a different material. These unofficial coats are not as nice as the official ones and are sold for only $4 and cost 60 cents to make. Assume that every medical professional who wanted to buy an official coat but could not get one agrees to buy an unofficial one instead and that no one buys the unofficial coats when there are still some official ones in stock. Finally assume no medical professional wants to buy a coat after January 15th. The discrete demand and their probabilities are listed in the table below.

Demand Probability F(Q) 1000 0.1 1150 0.15 1450 0.35 1600 0.3 2000. 0.1

(a) What is the probability that less than 1600 medical professionals come to the store wanting to buy an official coat?

(b) Suppose Universal Uniforms decides to order 1425 official coats in September. What is the probability that they will have run out by January 15th?

(c) Suppose Universal Uniforms decides to order 1500 official coats in September, but they have sold only 1450 of them by January 15. On that year, how much money do they make selling coats (official and unofficial)?

(d) Suppose Universal Uniforms decides to order 1500 official coats in September and that on December 15 they run out. Between December 15 and January 15, 100 more customers come to the store wanting to buy an official coat. On that year, how much money do they make selling coats (official and unofficial)?

(e) How many official coats would you recommend Universal Uniforms orders in September of each year?

(f) The firm who donates the coats increases their price to 60 cents per coat. How will this affect your answer to (e)? Explain whether it will increase or decrease without doing any computation.