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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

A company manufactures and sells DVDs Here are the equations they use in connection with their businessNumber of DVDs sold each day nx xSelling price for each D class=

Respuesta :

a. Revenue

[tex]R(x)=n(x)\cdot p(x)[/tex]

Substitute n(x) and p(x)

[tex]\begin{gathered} R(x)=x\cdot(8.5-0.05x) \\ \text{Simplify} \\ R(x)=8.5x-0.05x^2 \end{gathered}[/tex]

Answer a:

[tex]R(x)=8.5x-0.05x^2[/tex]

b. Cost

[tex]\begin{gathered} C(x)=f(x)+v(x) \\ So \\ C(x)=190+2x \end{gathered}[/tex]

Answer b:

[tex]C(x)=190+2x[/tex]

c. Profit

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

Simplify

[tex]\begin{gathered} P(x)=8.5x-0.05x^2-190-2x \\ P(x)=6.5x-0.05x^2-190 \\ \operatorname{Re}-order \\ P(x)=-0.05x^2+6.5x-190 \end{gathered}[/tex]

Answer c:

[tex]P(x)=-0.05x^2+6.5x-190[/tex]

d. Average cost

[tex]\begin{gathered} \bar{C}(x)=\frac{C(x)}{n(x)} \\ \bar{C}(x)=\frac{190+2x}{x} \end{gathered}[/tex]

Answer d:

[tex]\bar{C}(x)=\frac{190+2x}{x}[/tex]

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