Jacob Black prides himself on being the cookie King of the North. Small, freshly baked cookies are the specialty of his shops; day-old cookies are sold at a reduced price. Each dozen sells for $2.00 and costs $1.10. Cookies that are not sold at the end of the day are reduced to $1.00 per dozen and all of them are sold the following day as day-old merchandise. Jacob Black wants to know the number of cookies (in dozens) he should make each day. From an analysis of its past demands, the demand for cookies is estimated as:

Daily Demand

in Dozens        1800    2000    2200    2400    2600    2800    3000

Probability       0.05     0.10     0.20     0.30     0.20     0.10     0.05

(a) What is the optimal service level? What is the optimal number of cookies (in dozens) to make daily? Everything else being the same, what maximum salvage price per dozen will justify providing a 65% service level?

(b) Starting from (a), Jacob Black sets up an environmentally controlled chamber to keep unsold cookies fresh overnight at an estimated electricity cost of  $0.05 per dozen cookies. This enables him to raise the price of day-old cookies to $1.15 per dozen. He can still sell all the day-old cookies. What is the new optimal service level?

(c) Starting from (a), suppose Jacob Black offers a delivery service to the people who came to buy cookies after his shop had run out of cookies. The cookies will be prepared and delivered to their homes at no extra charge. The home delivery costs Jacob Black $0.50 per dozen cookies. What is the new optimal stocking level? 

(d) If the demand follows a normal distribution with mean 2400 and standard deviation 400. To provide a service level of 90%, what should be the optimal order size?