A Business Consultant Analyzing a Small Computer Company Finds That $x$

Essay

A business consultant analyzing a small computer company finds that if the company produces and sells $x$ microprocessors it has a total profit function (in thousands of dollars) given by $p ( x ) = 0.4 x ^ { 2 } - 0.0043 x ^ { 3 } + 7 x - 244$ , with $x$ (in hundreds), being the number of processors produced and sold annually.
(a) Graph the profit function and determine how many processors must be produced and sold in order to break even.
(b) What is the domain of the profit function where the company actually loses money?
(c) Estimate the number of processors that must be produced in order to give the company the largest possible profit.
(d) Estimate the largest profit.