Question

If a company has total costs

C(x) = 27,000 + 45x + 0.1x2
and total revenues given by
R(x) = 435x − 0.9x2,
find the break-even points. (Enter your answers as a comma-separated list.)

Answer 1

To find the break-even points, set the total revenue equal to the total cost and solve for x.

Step-by-step explanation:

To find the break-even points, we need to set the total revenue equal to the total cost and solve for x. In this case, we have:

R(x) = C(x)

435x - 0.9x^2 = 27,000 + 45x + 0.1x^2

Combining like terms and rearranging, we get:

1x^2 + 455x - 27,000 = 0

Using the quadratic formula, we can solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Plugging in the values from our equation, we get:

x = (-455 ± sqrt(455^2 - 4(1)(-27,000))) / (2(1))

Simplifying further, we get two break-even points: x = 60 and x = 375.