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)=x Selling price for each DVD: p(x)=11.5−0.07x Daily fixed costs: f(x)=160?

a.Revenue = R(x)= the product of the number of DVD's sold each day and the selling price of each DVD. R(x)=___

b.Cost = C(x)= the sum of the fixed costs and the variable costs. C(x)=___

c.Profit = P(x)= the difference between revenue and cost. P(x)=_

d. Average cost = ¯C¯ (x)= the quotient of cost and the number of DVD's sold each day. ¯C¯(x)=_

Answer 1

This is a bit out of my league but I'll give a go anyway:

Explanation:

a. Revenue:

`R(x)="number of dvd"xx"selling price"=n(x)xxp(x)=x xx(11.5-0.07x)=11.5x-0.07x^2`

b. Cost: here I think that the variable costs are the `0.07x` that appear in the daily price representing perhaps costs connected to demand and delivery (you need to order more dvds of an artist because there is more demand....for example); so we get:

`C(x)=160+0.07x`

c. Profit:

`P(x)=R(x)-C(x)=11.5x-0.07x^2-(160+0.07x)=11.43-0.07x^2-160`

d. Average cost:

`bar(C(x))=(C(x))/(n(x))=(160+0.07x)/x`