You have been hired as a marketing consultant to Johannesburg Burger Supply, Inc

Question

You have been hired as a marketing consultant to Johannesburg Burger Supply, Inc., and you wish to come up with a unit price for its hamburgers in order to maximize its weekly revenue. To make life as simple as possible, you assume that the demand equation for Johannesburg hamburgers has the linear form q = mp + b, where p is the price per hamburger, q is the demand in weekly sales, and m and b are certain constants you must determine.

(a) Your market studies reveal the following sales figures: When the price is set at $2.00 per hamburger, the sales amount to 7000 per week, but when the price is set at $4.00 per hamburger, the sales drop to zero. Use these data to calculate the demand equation.

(b) Now estimate the unit price that maximizes weekly revenue.
$  

Predict what the weekly revenue will be at that price.
$

Explanation / Answer

Given equation :

q = mp + b

When p = 2, q= 7000.

So, 7000 = m(2) + b

When p = 4, q = 0.

So, 0 = m(4) + b.

Solving both equations we get,

m = -3500 and b = 14000.

(a) So, the equation becomes : q = 14000 - 3500p.

Weekly revenue (R) = (sales)*(price per unit) = q*p = 14000p - 3500p2

For maximising revenue, its derivative must be equated to zero i.e

dR/dp = 0

14000 - 7000p = 0

(b) Therefore, p =2 = unit price that maximizes weekly revenue

(c) And, weekly revenue at this price = 7000*2 = 14000.

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