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6 September, 11:16

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).

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  1. 6 September, 12:46
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    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)
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