Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $7000 per month. Materials and labor for each helmet of this model are $25, and the company sells this helmet to dealers for $50 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.)

Required:

(a) For this helmet, write the function for monthly total costs C (x).

(b) Write the function for total revenue R (x). (c) Write the function for profit P (x).

C (x) = $ (7000+25x)

R (x) = $ (50x)

P (x) = $ (25x-7000)

Explanation:

Let x represent the number of helmets sold.

The fixed costs for one model of helmet are $7000 per month

Materials and labor for each helmet of this model are $25

(A) Monthly total costs C (x).

Monthly Total Cost, C (x) = Fixed Cost + Variable Cost

Fixed Cost=$7000

Variable Cost=$25 X number of helmets produced = $25x

Therefore, C (x) = $ (7000+25x)

(B) Total Revenue, R (x)

Selling Price Per Helmet = $50

Total Revenue = Selling Price Per Unit X Number of Units Sold = $50x

Therefore: R (x) = 50x

(C) Profit, P (x)

Profit=Selling Price - Cost Price

=Total Revenue-Monthly total costs = R (x) - C (x) = 50x - (7000+25x) = $ (25x-7000)

Therefore: P (x) = $ (25x-7000)