Answer:
Revenue function:

Profit function:

31 to 500 Gymnast Clothing are manufactured to make a profit.
Explanation:
The cost (in dollars) for a run of x pairs of cleats.

Gymnast Clothing sells the cleats at $100 per pair.
The Revenue (in dollars) for a run of x pairs of cleats.

Profit = Revenue - Cost



We need to find how many should Gymnast Clothing manufacture to make a profit.


From the given figure it is clear that P(x) is greater than or equal to 0 for 30.931 ≤ x ≤ 889.069.
The value of x can not be more than 500.
31 ≤ x ≤ 500
31 to 500 Gymnast Clothing are manufactured to make a profit.