Question

A company manufactures and sells DVD's. Here are the equations they use in connection with their business.Number of DVD's sold each day: n(x) = xSelling price for each DVD: p(x) = 8.5 -0.05xDaily fixed costs: f(x) = 190Daily variable costs: v(x) = 2xFind the following functions.a. Revenue = R(x) = the product of the number of DVD's sold each day and the selling price of each DVD.R(x)Previewb. Cost = C(z) - the sum of the fixed costs and the variable costs.C(x)Previewc. Profit=P(x) = the difference between revenue and cost.P(x) =Previewd. Average cost = (x) - the quotient of cost and the number of DVD's sold each day.(1)Preview

Answer 1

a. Revenue

`R(x)=n(x)\cdot p(x)`

Substitute n(x) and p(x)

`\begin{gathered} R(x)=x\cdot(8.5-0.05x) \\ \text{Simplify} \\ R(x)=8.5x-0.05x^2 \end{gathered}`

Answer a:

`R(x)=8.5x-0.05x^2`

b. Cost

`\begin{gathered} C(x)=f(x)+v(x) \\ So \\ C(x)=190+2x \end{gathered}`

Answer b:

`C(x)=190+2x`

c. Profit

`\begin{gathered} P(x)=R(x)-C(x) \\ P(x)=8.5x-0.05x^2-(190+2x) \end{gathered}`

Simplify

Answer c:

`P(x)=-0.05x^2+6.5x-190`

d. Average cost

`\begin{gathered} \bar{C}(x)=(C(x))/(n(x)) \\ \bar{C}(x)=(190+2x)/(x) \end{gathered}`

Answer d:

`\bar{C}(x)=(190+2x)/(x)`