Question

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).

Answer 1

Answer:

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)