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 3,000 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.

q = ____

 

(b)

Now, estimate the unit price that maximizes weekly revenue.

$ ___

Predict what the weekly revenue will be at that price.

$ ___

Answer 1

(3,2) and (0,4) are two points on a line with slope= (4-2)/-3 = -2/3 = (P-4)/(q-0)

q = -3P/2 + 6 is the demand curve with P measured in dollars and q in thousands. m=-3/2, b = 6

Revenue = Pq = -3P^2/2 + 6P

R' = -3P + 6 =0

P = $2 is the revenue maximizing price

R = -3(2)^2/2 +6(2) = 6 thousand dollars = $6,000 = max revenue

graph the two points, extend a straight line through them to the x axis

the x intercept is 6 or the point (6,0). the midpoint of that line segment is (3,2)

representing the revenue maximizing point with 3 representing 3,000 sales and 2 as $2 price