Question

The monthly cost of operation at a company, C, given in dollars as a function of the number of units produced per month, u, is given below.

C = $3,173 + $31u

If the company wants to keep the cost of operation under $18,000 per month, what is the maximum number of units they can produce?
A.
4,781
B.
4,780
C.
479
D.
478

Answer 1

To find the maximum number of units \( u \) that the company can produce while keeping the cost of operation under $18,000, we can set up the following inequality based on the cost function \( C \):

\[
C = 3,173 + 31u < 18,000
\]

Now, we can solve for \( u \):

1. Subtract 3,173 from both sides:

\[
31u < 18,000 - 3,173
\]

\[
31u < 14,827
\]

2. Divide both sides by 31:

\[
u < \frac{14,827}{31}
\]

Calculating that gives:

\[
u < 478.0323
\]

Since \( u \) must be a whole number, we round down to the nearest whole number:

\[
u \leq 478
\]

Thus, the maximum number of units that can be produced while keeping costs under $18,000 is:

**D. 478**