Gymnast clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. its cost (in dollars) for a run of x pairs of cleats is c(x) = 2750 + 8x + 0.1x2 (0 ≤ x ≤ 500). gymnast clothing sells the cleats at $100 per pair. find the revenue and profit functions. how many should gymnast clothing manufacture to make a profit?

Revenue function:

Profit function:

31 to 500 Gymnast Clothing are manufactured to make a profit.

Step-by-step 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.