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 3090 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 = Incorrect: Your answer is incorrect.
p=2.30 per burger
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To determine the demand equation, we need to find the values of m and b in the equation q = mp + b.
Given the sales figures:
- When the price is $2.00 per hamburger, the sales amount to 3090 per week.
- When the price is $4.00 per hamburger, the sales drop to zero.
Using these two points, we can set up a system of equations:
1) When p = $2.00, q = 3090:
3090 = 2m + b
2) When p = $4.00, q = 0:
0 = 4m + b
To solve this system of equations, we can subtract equation 2 from equation 1:
3090 = 2m + b
0 = 4m + b
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3090 = -2m
From this equation, we can solve for m:
-2m = 3090
m = -1545
Substituting this value of m into equation 2, we can solve for b:
0 = 4(-1545) + b
0 = -6180 + b
b = 6180
Therefore, the demand equation for Johannesburg hamburgers is q = -1545p + 6180.
To calculate the demand equation, we need to find the values of the constants m and b in the equation q = mp + b using the given sales figures.
Let's start by finding the slope (m) of the demand equation:
Using the two given points (p = $2.00, q = 3090) and (p = $4.00, q = 0), we can find the slope (m) using the formula:
m = (q2 - q1) / (p2 - p1)
Substituting the values:
m = (0 - 3090) / ($4.00 - $2.00)
m = (-3090) / ($2.00)
m = -1545
Now that we have the value of m, we need to find the intercept (b) of the demand equation. We can choose any of the given points to substitute into the equation and solve for b.
Let's substitute the point (p = $2.00, q = 3090):
3090 = (-1545)($2.00) + b
3090 = -3090 + b
b = 3090 + 3090
b = 6180
Therefore, the demand equation for Johannesburg hamburgers is:
q = -1545p + 6180