Question

The revenue and operating cost of a car wash facility are given by () = 13 − 0.72 and() = 2.5 + 3.5, where x represents the number of cars washed. What is the profit when 10 cars are washed?

Answer 1

Step-by-step explanation:

Given;

We are given the revenue and cost function of a car wash facility as follows;

`\begin{gathered} Revenue: \\ R(x)=13x-0.7x^2 \\ Cost: \\ C(x)=2.5x+3.5 \end{gathered}`

Also, we are told that in this function, x represents the number of cars washed.

Required;

We are required to calculate the profit when 10 cars are washed.

Step-by-step solution;

To begin, we will take note that the profit function is given as;

`Profit=Revenue-Cost`

Therefore, to determine the profit at any level of input x, we would have;

`P(x)=R(x)-C(x)`

We now substitute the values given;

`P(x)=(13x-0.7x^2)-(2.5x+3.5)`
`P(x)=13x-0.7x^2-2.5x-3.5`

Notice how the negative sign is distributed among the two values in the right parenthesis.

`P(x)=10.5x-0.7x^2-3.5`

We can now determine the profit when 10 cars are washed, that is, when x = 10.

`P(10)=10.5(10)-0.7(10)^2-3.5`
`P(10)=105-0.7(100)-3.5`
`P(10)=105-70-3.5`
`P(10)=31.5`

ANSWER:

The profit from washing 10 cars therefore will be $31.5