Q1. Johnson Electronics (JE) sells electrical and electronic components through catalogs. Catalogs are updated and printed twice every year. Each printing run incurs a fixed cost of $5,000, which involves catalog design cost and printing setup cost. The variable production cost is $5 per catalog. Annual demand for catalogs is estimated to be normally distributed with a mean of 16,000 and a standard deviation of 4,000. Data indicate that, on average, each customer ordering a catalog generates a profit of $35 from sales.

1. How many catalogs should be printed in each run? 2. Suppose that each unsold catalog can be sold to a recycling company for a price of $1. What is the optimal ordering quantity? 3. Finally, suppose that the deal with the recycling company is over, but JE signs an agreement with the printing company so that, if they run out of catalogs, they can do just-in-time printing and delivery at a cost of $15 per catalog.

Q2. The UTD cafeteria offers scones for $1.5 each from 8 am to 3 pm. The scones are ordered from their supplier at the start of each day and delivered before the store opens. The supplier charges 75 cents per scone. If at 3 pm, some scones are left unsold, the cafeteria people sell off the remaining scones for 50 cents each. Assume that all leftover scones are always sold by 4 pm when the cafeteria closes. If a customer asks for a scone before 3 pm but the cafeteria has run out, the customer always buys a bag of chips for $1 instead (after 3 pm, the customer does not buy anything instead). Assume the chips are always in stock and they are purchased from the same supplier for 40 cents each. Demand for scones before 3 pm at the cafeteria is variable but can only take values between 40 and 50, with probabilities given in the following table.

Number of customers Probability 40 /0.05 41 /0.05 42 /0.15 43/ 0.2 44 /0.15 45 /0.1 46 /0.1 47 /0.1 48 /0.05 49 /0.025 50 /0.025.

a. What is the expected number of customers who want to buy a scone on a given day? b. Yesterday the cafeteria ordered 45 scones, and 49 customers came wanting to buy a scone between 8 am and 3 pm. What was their profit (including, if any, the profit on chips sold instead of scones)? c. How much is the underage cost? d. How much is the overage cost? e. What is the optimal number of scones to order at the start of each day? f. Given the order quantity in part e, what is the probability that the cafeteria cannot satisfy all the demand for scones before 3 pm?

Q3. You are in charge of the annual banquet for the Football Boosters Club at your college. One week before the banquet you must make a commitment for the number of dinners. The price for these dinners will be $7 each. If fewer people show up than the committed number, you are still required to pay for the full number. If more people attend than your committed number, they will be served at a cost of $12 each. For example, if you commit to 200 people and 200 or fewer show up, you still have to pay $1,400. If more than 200 attend, you pay $1,400 plus $12 for each dinner in excess of 200. Your judgment about the number attending can be described by a normal probability distribution with a mean of 400 people and a standard deviation of 100.

a) Suppose the cost of the banquet is being borne entirely by the Alumni Association, and your objective is to minimize the cost, given that all who attend will be served. How big a prior commitment for dinners should you make to the hotel? b) Suppose there is a charge of $10 for every person attending. Your objective is to maximize the profit from the banquet. In this case, how large a prior commitment should you make to the hotel?