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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).

Respuesta :

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

Step-by-step explanation:

Since we have given that

Unit price is expressed as

[tex]p=480.03x^2+1[/tex]

Let x be the number of units of a thousands.

So, Revenue function is given by

[tex]R(x)=px\\\\R(x)=x(480.03x^2+1)\\\\R(x)=480.03x^3+x[/tex]

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

Marginal revenue function becomes,

[tex]R'(x)=3\times 480.03x^2+1\\\\R'(x)=1440.09x^2+1[/tex]

(c) Compute R'(2).

[tex]R'(2)=1440.09(2)^2+1\\\\R'(2)=5760.36+1\\\\R'(2)=5761.36[/tex]

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

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