Scenario 16.2 - Card Table Vendor
The traditional fundraiser for the student chapter of APICS is pint mason jars filled with a tangy barbecue sauce that the club sponsor whips up in his kitchen. Club officers set up a card table in the atrium of the business building and take turns staffing it for the duration of the barbecue season, which is four months. Eighteen sad 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 400-p?, in the second month as 400-1.4p?, in the third month 400-1.8p?, and in the fourth month 400-2.2p?.
-What is the expected revenue if the student APICS chapter uses dynamic pricing?
A) $83,975.47
B) $84,349.06
C) $84,719.84
D) $85,209.84

Question

Quizplus · Accepted Answer

The correct answer is A because the expected revenue is $83,975.47. This is calculated by taking the average demand for each month and multiplying it by the price for that month. The average demand for the first month is 400-p?, so the revenue for that month is (400-p?) * p? = 400p? - p^3. The average demand for the second month is 400-1.4p?, so the revenue for that month is (400-1.4p?) * 1.4p? = 560p? - 1.96p^3. The average demand for the third month is 400-1.8p?, so the revenue for that month is (400-1.8p?) * 1.8p? = 720p? - 3.24p^3. The average demand for the fourth month is 400-2.2p?, so the revenue for that month is (400-2.2p?) * 2.2p? = 880p? - 4.84p^3. The total revenue for the four months is the sum of these four revenues, which is 400p? - p^3 + 560p? - 1.96p^3 + 720p? - 3.24p^3 + 880p? - 4.84p^3 = 2560p? - 11.04p^3. The expected revenue is the average revenue, which is 2560p? - 11.04p^3 / 4 = 640p? - 2.76p^3. The optimal price is the price that maximizes revenue, which is found by taking the derivative of revenue with respect to price and setting it equal to zero. The derivative of revenue with respect to price is 640 - 8.28p^2, so setting this equal to zero and solving for p gives p = 9. The expected revenue is then 640(9) - 2.76(9)^3 = $83,975.47.