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 is linear. (a) Your market studies reveal the following sales figures: When the price is set at $2.00 per hamburger, the sales amount to 6000 per week, but when the price is set at $4.00 per hamburger, the sales drop to zero. Use these data to find the linear demand function q (p), where p is the price per hamburger and q is the number of hamburgers they sell at that price per week.

Question

Mathematics

Ralph

15 June, 03:20

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 is linear. (a) Your market studies reveal the following sales figures: When the price is set at $2.00 per hamburger, the sales amount to 6000 per week, but when the price is set at $4.00 per hamburger, the sales drop to zero. Use these data to find the linear demand function q (p), where p is the price per hamburger and q is the number of hamburgers they sell at that price per week.

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Answers (1)

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Eliezer Webb · Answer 1

q (p) = - 3000p+12000

Step-by-step explanation:

For the function to be linear,

q (p) = mp + c

where

q (p) : number of hamburgers sold

p: price per hamburger

m: gradient of the function

c: constant of the function

q (p) = 6000 when p=2

6000=2m+c ... equation I

0=4m+c

c=-4m ... equation II

Substitute value of c in equation I

6000=2m-4m

m = - 3000

c=12000

q (p) = - 3000p+12000