Question

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. Blinded by their jealousy, 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-p1, in the second month as 20-1.4p2, in the third month 20-1.8p3, and in the fourth month 20-2.2p4.

I. The components needed to produce a computer clock cost twenty-five cents. What should the price of the computer clocks be in the first month of the selling season?

II. The components needed to produce a computer clock cost twenty-five cents. What should the price of the computer clocks be in the third month of the selling season?

III. The components needed to produce a computer clock cost twenty-five cents. How many clocks should the AITP club produce?

IV. The components needed to produce a computer clock cost twenty-five cents. What is the expected profit if the AITP club sponsor produces the optimal number of clocks?

Answer 1

Decision variables:

Let p1,p2,p3,p4 represent the cost/clock for months 1-4 respectively.

Constraints:

p1,p2,p3,p4>=0

Objective Function:

Maximize Profit

Profit=(20-p1)*p1+(20-1.4p2)*p2+(20-1.8p3)*p3+(20-2.2p4)*p4-0.25*(20-p1+20-1.4p2+20-1.8p3+20-2.2p4)

excel model:

Solver solution:

i) price in first month =	$                           10.12
ii) price in third month =	$                              5.68
iii) total clocks to produce (sum of demands for the four months)=	39
iv) expected profit=	$                         262.54