Question

A company produces very unusual CD's for which the variable cost is $ 20 per CD and the fixed costs are $

50000. They will sell the CD's for $ 44 each. Let u be the number of CD's produced.
Write the total cost C as a function of the number of CD's produced.
C=$
Write the total revenue R as a function of the number of CD's produced.
R= $
Write the total profit P as a function of the number of CD's produced.
P= $
Find the number of CD's which must be produced to break even.
The number of CD's which must be produced to break even is

Answer 1

1) $30,000 + $12x

(2) $50x

(3) $38x - $30,000

(4) 790 CD's to break even

Given that,

Variable cost = $12 per CD

Fixed cost = $30,000

Selling price = $50 each

Let x be the number of CD's produced,

(1) Total cost function:

C(x) = Fixed cost + Variable cost

= $30,000 + $12x

(2) Total revenue:

R(x) = Units produced × selling price of each unit

= $50x

(3) Total profit:

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

= $50x - ($30,000 + $12x)

= $50x - $30,000 - $12x

= $38x - $30,000

(4) Number of CD's which must be produced to break even:

Total profit = 0

$38x - $30,000 = 0

x = $30,000 ÷ $38

= 789.47 or 790 CD's to break even.

Hope this helps! :)