Final answer:
The company can produce a maximum of 478 whole units to keep the monthly cost of operation under $18,000, according to the cost function C = $3,173 + $31u; solving for u when C is less than or equal to $18,000.
Step-by-step explanation:
To determine the maximum number of units the company can produce while keeping the cost of operation under $18,000 per month, we use the given cost function C = $3,173 + $31u, where C represents the monthly cost and u represents the number of units produced. We need to solve for u when C is less than or equal to $18,000.
First, we substitute $18,000 for C and solve for u:
- $18,000 = $3,173 + $31u
- $18,000 - $3,173 = $31u
- $14,827 = $31u
- u = $14,827 / $31
- u = 478.29
Since the company cannot produce a fraction of a unit, the maximum number of whole units they can produce is 478 units.