Chapter 7, Problem 76RE

To determine

To Find: the breakeven point where the total cost equations C and total revenue R are given

Answer to Problem 76RE

The numbers of units a company must sell to break even are 8.

Explanation of Solution

Given:

The given equations for the total cost C and total revenue R are $C=5.5\sqrt{x}+10000,R=4.22x$

Concept Used:

For the breakeven point to be found the total cost and the total revenue are to be equated. The point when these two are equal is known as breakeven point.

Calculation:

As per the given problem when both the equations are equated

  $5.5\sqrt{x}+10000=4.22x$

Let us substitute $\sqrt{x}=y$ then the equation changes as $5.5y+10000=4.22y^2$

Now by solving this quadratic equation

  $\begin{array}{l}4.22y^2-5.5y-10000=0\\ y=49.33,-48.03\end{array}$

Now by substituting this y value which is positive in the above equation we get the number of units. As the units will not be negative we should take positive value.

  $\begin{array}{l}\sqrt{x}=y\\ $ x={(49.33)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$x=7.02\\ x=8\end{array}$

Conclusion:

The numbers of units a company must sell to break even are 8.