Question

Hi i forgot how i did this last time and i keep getting the wrong answers

Answer 1

We have to find the expression for the profit in function of the number of units x.

We have an expression for the revenue R(x) and for the cost C(x):

`\begin{gathered} R(x)=5x^2+2x-80 \\ C(x)=5x^2-x+100 \end{gathered}`

If the profit, that we will call P(x), is the difference between the revenue and the cost, we can calculate it like this:

`\begin{gathered} P(x)=R(x)-C(x) \\ P(x)=(5x^2+2x-80)-(5x^2-x+100) \\ P(x)=5x^2+2x-80-5x^2+x-100 \\ P(x)=(5x^2-5x^2)+(2x+x)+(-80-100) \\ P(x)=3x-180 \end{gathered}`

We can now calculate the profit for the sale of 1000 videogames (x = 1000) as:

`P(1000)=3\cdot1000-180=3000-180=2820`

Answer:

a) P(x) = 3x - 180

b) The profit is $2820