problem 1
 
A) Debbie is the purchasing manager of Campus Bookstore at Phoenix’s University. Every year in March she desires to plan on the number of ‘Graduation Rings’ the Bookstore should stock. The “Graduation Rings’ are specialty rings made by Tiffany and have the year of graduation engraved on them. Each ring costs $150/- and is sold for $300/-. By July if the “Graduation Rings” were not sold a jeweler would purchase them at a price of $50/- per ring. Rings which didn’t sell in one year can’t be stocked and sold the subsequently year. Based on past history Debbie knew that the demand for the “Graduation Rings” could range from 2 to 7. She computed the probability for the various values of demand to be as follows
 
Demand in units    2    3     4        5      6       7
Probability           0.1  0.1  0.2    0.3    0.2    0.1
 
Based on this information, what is the optimal number of “Graduation Rings” Debbie should buy for the Campus Bookstore at Phoenix’s University?  What is Bookstore’s anticipated profit, given the optimal decision?

B) It costs Tiffany $70 to make the rings. Tiffany’s is willing to offer the ‘Graduation Rings” to the Campus Bookstore at $70, provided the Campus Bookstore is willing to share the revenue. Tiffany suggests that the Campus Bookstore can retain 60% of the revenue and must pass on 40% of the revenue to Tiffany. Should the Campus Bookstore at Phoenix’s University take up this offer? Are both the Campus Bookstore and Tiffany’s better off in this scheme? Can you identify a range of manufacturer revenue share that makes sure both parties are better off than before? Show the computation.

problem 2
 
A) You decide to start a small seated cafe, named Kings Lunch which operates in Phoenix University and does business only throughout the short lunch hour from noon to 1 PM. In your business plan you approximate the everyday demand forecast using a normal distribution with mean 53 and standard deviation 8. You estimate customers will spend $20 on an average, generating a gross profit of $6. On the other hand when more customers come to Kings Lunch than who can be seated then customers will have to be turned away resulting in lost sales. Phoenix University is willing to lease each seat for 250 days in the year at $1000 per seat (that is, $4 per day). What is optimal number of seats you must lease?

B) Phoenix University now mandates which you must serve at least 80% of customers. This implies that you can turn away customers at most 20% of the time! What should the optimal number of seats you must now lease?