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).
Accepted Solution
A:
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.