Question 1

A) Debbie is the purchasing manager of the Campus Bookstore at Phoenix's University. Every year in March she needs 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 jeweller would buy them at a price of $50/- per ring. Rings which did not sell in one year cannot be stocked and sold the next year. Based on past history Debbie knew that the demand for the "Graduation Rings" could range from 2 to 7. She calculated 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 expected profit, given the optimal decision?

B) It costs Tiffany $70 to make the rings. Tiffany's is willing to provide 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 should 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 ensures both parties are better off than before? Show the calculations.

Question 2

A) You decide to start a small seated cafe, named Kings Lunch which operates in Phoenix university and does business only during the short lunch hour from noon to 1 PM. In your business plan you approximate the daily 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 (i.e. $4 per day). What is the optimal number of seats you should lease?

A) Phoenix University now mandates that you should serve atleast 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 should now lease?