Problem
The student chapter of the Association of Information Technology Professionals(AITP) notices the success that the APICS student chapter has with their traditional barbecue sauce fundraiser. The club officers decide to sell a competing product, clocks made out of junk computer parts that the club sponsor whips up in his garage. Club officers set up a card table in the atrium of the business building and take turns staffing it for the duration of the computer clock season, which is four months. Twenty-five years of experience have revealed that demand varies depending on the month of the season. Customer demand in the first month can be described as 20-pl, in the second month as 20-1.4p2, in the third month 20-1.8p3, and in the fourth month 20-2.2p4. The components needed to produce a computer clock cost twenty-five cents.
A. Assume the club officers want to charge the same price over the four months. Find the single price which maximizes overall profit. How many clocks they need to have at the beginning of the season to satisfy demand?
B. If the club officers want to charge dynamic prices that vary by month, what should the price of the computer clocks be in the first month and third month of the selling season?
C. How many clocks they need to have at the beginning of the season using dynamic prices? What is the expected profit?
D. Suppose the components are only available to produce 30 clocks at most, which is less than the optimal quantity needed at the beginning of the season. How would this constraint affect the dynamic prices conceptually? Show qualitative analysis; you don't need to calculate the numbers.