Question

The quantity of Sensitech laser gaming mice demanded each month is related to the unit price by the equation p = 480.03x2 + 1 (0 ≤ x ≤ 20) where p is measured in thousands of dollars and x in units of a thousand.(a) Find the revenue function R.(b) Find the marginal revenue function R'.(c) Compute R'(2).

Answer 1

Answer: a)
`p=480.03x^2+1`, b)
`R'(x)=1440.09x^2+1` c) $5761.36.

Explanation:

Since we have given that

Unit price is expressed as

`p=480.03x^2+1`

Let x be the number of units of a thousands.

So, Revenue function is given by

`R(x)=px\\\\R(x)=x(480.03x^2+1)\\\\R(x)=480.03x^3+x`

.(b) Find the marginal revenue function R'..

Marginal revenue function becomes,

`R'(x)=3* 480.03x^2+1\\\\R'(x)=1440.09x^2+1`

(c) Compute R'(2).

`R'(2)=1440.09(2)^2+1\\\\R'(2)=5760.36+1\\\\R'(2)=5761.36`

Hence, a)
`p=480.03x^2+1`, b)
`R'(x)=1440.09x^2+1` c) $5761.36.