Question

You invest in a new technology company. The cost includes an overhead of $30,000, p production costs of $2500 per item produced. Each item sells for $3125. a. Write the cost function, C. b. Write the revenue function R. C. Determine the break-even point. Describe what it means.

Answer 1

A. C(x) = 30.000 + 2500x

B. R(x) = 3125x

C. 48 items break even point

Explanation:

A. The cost function C(x) is fixed cost plus variable cost.

In this case overhead works as fixed cost, we can write:

C(x) = 30.000 + 2500x

B. Revenue R(x) would be the price multiplied by quantity of items (x).

R(x) = 3125x

C. Break even point

To get the break even point we set R(x) = C(x) and find the value of x.

R(x) = C(x)

3125x = 30.000 + 2500x

3125x-2500x=30.000

625x=30.000

x=30.000/625

x=48

It means when you sell 48 items the costs will even revenue. So if you sell more than 48, then it's going to be profitable. If you sell less than 48, you will be losing money.