A certain fast food restaurant wants to determine the increase in revenue per cheeseburger if sales are $45000 . Let the function p=120000-x/30000 represent the price for x cheeseburgers.
revenue is quantity * price, so
r(x) = x*p(x) = 120000x - x^2/30000
r'(x) = 120,000 - x^2/15,000
so ∆r ≈ r'(x) * ∆x
so find x when r(x) = 45,000 and then use ∆x = 1
To determine the increase in revenue per cheeseburger, we need to find the derivative of the revenue function with respect to the number of cheeseburgers sold. In this case, the revenue function is given by:
R(x) = p * x
where R(x) is the revenue, p is the price per cheeseburger, and x is the number of cheeseburgers sold.
From the given function p = (120000 - x)/30000, we can substitute this into the revenue function to get:
R(x) = [(120000 - x)/30000] * x
To find the derivative of R(x), we can multiply out the expression and simplify:
R(x) = (120000x - x^2)/30000
Now, let's differentiate R(x) with respect to x:
dR/dx = (d/dx)(120000x - x^2)/30000
= (120000 - 2x)/30000
= (120000 - 2x)/30000
This derivative represents the increase in revenue per cheeseburger sold at a given point. To find the increase in revenue per cheeseburger when sales are $45000, we can substitute x = 45000 into the derivative:
dR/dx = (120000 - 2(45000))/30000
= (120000 - 90000)/30000
= 30000/30000
= 1
Therefore, the increase in revenue per cheeseburger when sales are $45000 is $1.
To determine the increase in revenue per cheeseburger, we need to calculate the change in revenue when the number of cheeseburgers sold increases by one.
The given function represents the price, p, for x number of cheeseburgers. It is defined as p = (120000 - x) / 30000.
Revenue, R, is calculated by multiplying the price by the quantity sold. So, R = p * x.
We are given that the sales are $45000. Therefore, we can substitute this value for R in the equation and solve for x:
45000 = p * x (equation 1)
Substituting the equation for p, we get:
45000 = ((120000 - x) / 30000) * x
To solve this equation for x, we can multiply both sides by 30000 to remove the fraction:
45000 * 30000 = (120000 - x) * x
Now, we can simplify and solve for x.