If the total revenue function for a computer is R(x) = 1600x − 26x2 − x3, find the level of sales, x, that maximizes revenue and find the maximum revenue in dollars.

Question

x= ________ computers

R(x) = $ ______ ?

Answer 1

Calculate dR/dx and solve for x using quadratic formula, with dR/dx = 0 criterion for critical point.

You can calculate R(x) for both of the critical points. One will be a local max and the other a local min. You want to keep the domain to x > 0. The positive value will be a global max for this domain because x(0) = 0 and R --> -inf as x--> inf. You can also take the 2nd derivative to see that the sign is negative at the critical point -- implying a maximum.