Question

The wheely fast co. Makes custom skateboards for professional riders. They model their profit with the relation P=-2b^2 + 14b - 20, where b is the number of skateboards they produce(in thousands) and P is the company's profit in hundred thousands of dollars. When does wheely fast break even?

Answer 1

The answer is below

Explanation:

Breakeven point is the point of balance where their is neither a loss or a profit. At the breakeven point, the revenue gotten from the sell of goods is equal to the cost of production of the goods, hence the profit is zero.

Given the profit function:

P=-2b² + 14b - 20

At breakeven P = 0, hence:

0 = -2b² + 14b - 20

-2b² + 14b - 20 = 0

-2b² + 10b + 4b - 20 = 0

-2b (b - 5) + 4(b - 5) = 0

(b - 5)(-2b + 4) = 0

b - 5 = 0; or -2b + 4 = 0

b = 5; or b = 2

Since b is in thousands, hence the company breaks even when the number of skateboards produced is either 2000 or 5000