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26 March, 00:56

A manufacturer of DVD players has monthly fixed costs of $9500 and variable costs of $55 per unit for one particular model. The company sells this model to dealers for $90 each.

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

C (x) =

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

R (x) =

(c) Write the function for profit P (x).

P (x) =

(d) Find C (240).

C (240) =

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Answers (1)
  1. 26 March, 01:23
    0
    (a) C (x) = 9500 + 55x

    (b) R (x) = 90x

    (c) P (x) = 35x - 9500

    (d) C (240) = $22,700

    All functions are measured in $.

    Explanation:

    The total revenue of an entity is a function of the number of units sold and the selling price per unit. The total cost is a function of the fixed cost and the variable cost (which is also a function of the units produced/sold). Profit is a function of sales and cost.

    Given that monthly;

    fixed costs = $9500

    variable costs = $55 per unit

    Selling price = $90 per unit

    Where x is the number of units

    total costs C (x) in $ = 9500 + 55x

    total revenue R (x) in $ = 90x

    profit P (x) in $ = 90x - (9500 + 55x)

    = 35x - 9500

    C (240) = 9500 + 55 (240)

    = $22,700
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