Question

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-p1, in the second month as 400-1.4p2, in the third month 400-1.8p3, and in the fourth month 400-2.2p4.

I. What should the price be in period 1?

II. What should the price be in period 3?

III. What is the expected revenue if the student APICS chapter uses dynamic pricing?

IV. 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?

V. 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 total revenue for the season's sales at the optimal price?

Answer 1

I. Expected Revenue in period 1, R1 = Expected demand * price = (400-p1)*p1 = 400p1-p1²

First order derivative of revenue function R1'(p1) = d((400p1-p1²)/dp1 = 400-2p1

For maximising revenue, equate this to 0, so 400-2p1 = 0

Solving for p1, we get, p1 = 400/2 = 200

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II. Expected Revenue in period 2, R2 = Expected demand * price = (400-1.4p2)*p2 = 400p2-1.4p2²

First order derivative of revenue function R2'(p2) = d((400p2-1.4p2²)/dp2 = 400-2.8p2

For maximising revenue, equate this to 0, so 400-2.8p1 = 0

Solving for p1, we get, p1 = 400/2.8 = 143

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