EXPLANATION:
Given;
We are given the revenue and cost function of a car wash facility as follows;
[tex]\begin{gathered} Revenue: \\ R(x)=13x-0.7x^2 \\ Cost: \\ C(x)=2.5x+3.5 \end{gathered}[/tex]
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;
[tex]Profit=Revenue-Cost[/tex]
Therefore, to determine the profit at any level of input x, we would have;
[tex]P(x)=R(x)-C(x)[/tex]
We now substitute the values given;
[tex]P(x)=(13x-0.7x^2)-(2.5x+3.5)[/tex][tex]P(x)=13x-0.7x^2-2.5x-3.5[/tex]
Notice how the negative sign is distributed among the two values in the right parenthesis.
[tex]P(x)=10.5x-0.7x^2-3.5[/tex]
We can now determine the profit when 10 cars are washed, that is, when x = 10.
[tex]P(10)=10.5(10)-0.7(10)^2-3.5[/tex][tex]P(10)=105-0.7(100)-3.5[/tex][tex]P(10)=105-70-3.5[/tex][tex]P(10)=31.5[/tex]
ANSWER:
The profit from washing 10 cars therefore will be $31.5
