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

question 33

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.

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Definitions:

Bond

An interest-bearing security that obligates the issuer to pay the bondholder a specified sum of money, generally at fixed intervals, and to repay the principal at maturity.

Maturity Date

The due date on which a loan or bond must be completely paid off, including principal and interest.

Interest Earned

The amount of income generated from an investment or the amount of interest accumulated on a financial asset over a period of time.

Bond Payable

A long-term debt instrument issued by a company, promising to pay the holder a specified amount of interest over a set period and to repay the principal on the bond's maturity date.