To find the break-even point for the given cost and revenue equations, we need to determine the number of units [tex]\( n \)[/tex] at which the cost equals the revenue. The given equations are:
[tex]\[
\begin{array}{l}
C = 94n + 534,000 \\
R = 168 n
\end{array}
\][/tex]
The break-even point is where Cost [tex]\( C \)[/tex] equals Revenue [tex]\( R \)[/tex]. Therefore, we set the equations equal to each other:
[tex]\[
94n + 534,000 = 168n
\][/tex]
Next, we need to solve for [tex]\( n \)[/tex]. To do this, we first isolate [tex]\( n \)[/tex] by moving all terms involving [tex]\( n \)[/tex] to one side of the equation. We can achieve this by subtracting [tex]\( 94n \)[/tex] from both sides:
[tex]\[
534,000 = 168n - 94n
\][/tex]
Simplify the right side of the equation:
[tex]\[
534,000 = 74n
\][/tex]
Now, solve for [tex]\( n \)[/tex] by dividing both sides of the equation by 74:
[tex]\[
n = \frac{534,000}{74}
\][/tex]
Perform the division to find the value of [tex]\( n \)[/tex]:
[tex]\[
n = 7216.216216216216
\][/tex]
Since we are asked to round to the nearest whole unit, we round 7216.216216216216 to:
[tex]\[
n \approx 7216
\][/tex]
Therefore, the break-even point is:
[tex]\[
d. 7216
\][/tex]
