Question

The linear cost and revenue functions are given as follows: C(x)=22x+479, R(x)=39x. To break even, the company needs to find the point at which the cost equals the revenue. What is the necessary number of items (x) to break even?

A) 22 items
B) 17 items
C) 11 items
D) 9 items

Answer 1

To determine the break-even point, the cost function C(x) is set equal to the revenue function R(x). After solving the equation, it is found that the company needs to sell 29 items to break even, indicating a possible error in the provided options.

Step-by-step explanation:

To find the necessary number of items (x) for the company to break even, we set the cost function equal to the revenue function:

C(x) = R(x) → 22x + 479 = 39x.

To find x, we will solve the equation:

1. Subtract 22x from both sides: 479 = 17x.
2. Divide both sides by 17 to find x: x = 479 / 17.
3. Simplify to find the value of x: x = 28.176.

Since x must be a whole number, it rounds up to 29 (as you cannot have a fraction of an item), but this value isn't one of the options presented. It seems there might be a typographical error in the question or the provided options, as none match the correct value.