Chapter 7.1, Problem 83E

To determine

To determine the cost and revenue function of the given information and hence find the solution of the equations both analytically and graphically.

Answer to Problem 83E

Thesolution of the given linear equations is $x=344$

Explanation of Solution

Given information: The given information is:

A software company invests $16,000 to produce each unit of software package for $9.45 and sell it for $55.95.

Also, calculate the number of units, where $R=C$

Calculation:

(a) Let $C(x)$ be the cost function and $R(x)$ be revenue function for each value of $x$ units

  $\text{Cost function: }C(x)=16000+9.45x$

  $\text{Revenue function: R}(x)=55.95x$

(b)  Using graphing utility to sketch the following functions:

  $\text{Cost function: }C(x)=16000+9.45x$ ;  $\text{Revenue function: R}(x)=55.95x$

The graph of the functions is:

  

From the above graph, it is concluded that both the functions are in straight line.

The given equations are:

  $C(x)=16000+9.45x;\text{R}(x)=55.95x$

For $R=C$

  $16000+9.45x=55.95x$

  $\Rightarrow 46.5x=16000$

  $\Rightarrow x=344.08\approx 344$

Hence, the number of units of software package to be sold, when $R=C$ is $x=344$