Famous Albert prides himself on being the Cookie King of the West. Small, freshly baked cookies are a specialty of his shop. Famous Albert has asked for help to determine the number of cookies he should make each day. From an analysis of past demand he estimates demand for cookies as
DEMAND PROBABILITY
1,800 dozen 0.05
2,000 0.10
2,200 0.20
2,400 0.30
2,600 0.20
2,800 0.10
3,000 0.05
Each dozen sells for $0.69 and costs $0.49, which includes handling and transportation. Cookies that are not sold at the end of the day are reduced to $0.29 and sold the following day as day-old merchandise.
a. Construct a net profit table similar to the one on page 395 of our textbook showing profit for each purchase decision and each demand event (this will be a seven-by-seven table).
b. What is the optimal number of cookies to bake? By what criteria?
c. Now arrive at your answer to part b by a second method, the method of marginal analysis (this will be much easier).