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) =

(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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