Certainly! Let's go through the process of finding the break-even point step-by-step.
We are given the following equations for cost [tex]\( C \)[/tex] and revenue [tex]\( R \)[/tex]:
[tex]\[ C = 20n + 134,000 \][/tex]
[tex]\[ R = 160n \][/tex]
The break-even point occurs where the cost equals the revenue, meaning [tex]\( C = R \)[/tex]. Therefore, we set the two equations equal to each other:
[tex]\[ 20n + 134,000 = 160n \][/tex]
To isolate [tex]\( n \)[/tex], we need to get all the [tex]\( n \)[/tex] terms on one side of the equation and the constants on the other side. We start by subtracting [tex]\( 20n \)[/tex] from both sides:
[tex]\[ 134,000 = 160n - 20n \][/tex]
This simplifies to:
[tex]\[ 134,000 = 140n \][/tex]
Now, solve for [tex]\( n \)[/tex] by dividing both sides of the equation by 140:
[tex]\[ n = \frac{134,000}{140} \][/tex]
Performing the division, we get:
[tex]\[ n = 957.1428571428571 \][/tex]
We round this result to the nearest whole unit:
[tex]\[ n \approx 957 \][/tex]
So the break-even point, rounded to the nearest whole unit, is 957.
Therefore, the correct answer is:
d. 957
