Cost, Revenue, and Profit A company invests $98,000 for equipment to produce a new product. Each unit of the product costs $12.20 and is sol

Question

Cost, Revenue, and Profit A company invests $98,000 for equipment to produce a new product. Each unit of the product costs $12.20 and is sold for $16.98. Let x be the number of units produced and sold. (a) Write the total cost C as a function of x. C(x) = 98000+16.98x (b) Write the revenue R as a function of x. R(x) = 207.156 (c) Write the profit P as a function of x. P(x) = 4.78

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Thành Đạt 5 years 2021-08-06T03:58:28+00:00 1 Answers 61 views 0

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  1. Eirian
    0
    2021-08-06T04:00:02+00:00
    Reply

    Given:

    Investment on equipment = $98,000

    Cost of each unit = $12.20

    Selling price of each unit = $16.98.

    To find:

    (a) The total cost C as a function of x.

    (b) The revenue R as a function of x.

    (c) The profit P as a function of x.

    Solution:

    Let x be the number of units produced and sold.

    We have,

    Fixed cost = $98,000

    Variable cost = $12.20x

    Total cost = Fixed cost + Variable cost

    C(x)=98000+12.20x

    Therefore, the cost function is C(x)=98000+12.20x.

    Selling price of each unit = Revenue from each unit =  $16.98.

    Total revenue = Revenue from x units

    R(x)=16.98x

    Therefore, the revenue function is R(x)=16.98x.

    Profit = Revenue – Cost

    P(x)=R(x)-C(x)

    P(x)=16.98x-(98000+12.20x)

    P(x)=16.98x-98000-12.20x

    P(x)=4.78x-98000

    Therefore, the profit function is P(x)=4.78x-98000.

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