Question

The marketing research department for a company that manufactures and sells notebook computers established the following revenue and cost functions:

R(x)=54x−2x2
C(x)=30x+54

where R(x)and C(x) are in millions of dollars.

For what values of x will the company break even?

Answer 1

To find the break-even point, set the total revenue equal to total cost and solve for the quantity. In this case, the company will break even when they sell 9 million notebook computers.

Step-by-step explanation:

To determine the break-even point for the company, we need to find the quantity of notebooks sold which result in zero profit. At the break-even point, total revenue is equal to total cost. We can set up the equation:

R(x) = C(x)

54x - 2x^2 = 30x + 54

Simplifying and rearranging the equation, we get:

2x^2 - 24x - 54 = 0

Solving this quadratic equation, we find that the company will break even at x = 9 units. Therefore, the company will break even when they sell 9 million notebook computers.