Question

A guitar factory has a cost of production C(x) = 100x + 56000 , where is the number of guitars produced . If the company needs to break even after 150 units sold, at what price should they sell each guitar ? Use the variable p to represent the price Round up to the nearest dollar .

Answer 1

473.33 units

Explanation:

The breakeven point is the level of production at which the costs of production equal the revenues for a product. So, considering P the price of a guitar unit, we have that:

C(150) = 150.P

P = C(150)/150

P = (100.150 + 56000) / 150

P = (15000 + 56000) / 150

P = 71000/150

P ~ 473.33 units of currency per guitar

Answer 2

Explanation:

If the company wants to just break even, that means that the cost to produce 150 guitars is equal to the price they charge to make a 0 profit. The cost of 150 guitars is

C(150) = 100(150) + 56000 and

C(150) = 71000. That's how much it costs to produce 150 guitars. If they want to make nothing at all, they have to sell the 150 guitars for

p(x) = 71000/150 so

p(x) = 473.33 or 474