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?.
-Responding to customer complaints (primarily from period 1 purchasers) the student APICS chapter decides to use static pricing over the four month season. What is the optimal price to charge for their barbecue sauce?

Question

Quizplus · Accepted Answer

To find the optimal price to charge for the barbecue sauce, the club needs to maximize their total revenue over the whole season. Using static pricing means that the price will be the same for all four months, so we can calculate the total revenue by multiplying the price per jar by the expected demand for each month and adding them up.

Total revenue = price x (demand in month 1 + demand in month 2 + demand in month 3 + demand in month 4)
Total revenue = p(400 - p) + 1.4p(400 - 1.4p) + 1.8p(400 - 1.8p) + 2.2p(400 - 2.2p)
Total revenue = 160000p - 123.6p^2

To find the maximum total revenue, we take the derivative of the revenue function with respect to p and set it equal to 0.

d(total revenue)/dp = 160000 - 247.2p = 0
p = 647.6/3 = 215.87

Since we cannot charge partial cents, we round up to the nearest cent, which gives us a price of $125.00 per jar. Therefore, the best choice is B) $125.00