A company produces very unusual CD's for which the variable cost is $ 12 per CD and the fixed costs are $ 30000. They will sell the CD's for $ 50 each. Let be the number of CD's produced.

1) Write the total cost as a function of the number of CD's produced.

2) Write the total revenue as a function of the number of CD's produced.

3) Write the total profit as a function of the number of CD's produced.

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

(1) $30,000 + $12x

(2) $50x

(3) $38x - $30,000

(4) 790 CD's to break even

Explanation:

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.