The revenue for a business, as a function of units produced, x, is shown below by R(x). C(x) represents the cost of producing x units. Calculate the profit function and then determine how many units must be produced for the business to break even.

Answers

Answer 1

Answer:

Step-by-step explanation:

We are not given the Revenue and the Cost function but we can assume the folloeing functions for the purpose of the question.

Let R(x) = 300x-2x²

C(x) = 5000+4x

Profit = Revenue - Cost

P(x) = R(x) - C(x)

P(x) = 300-2x - (5000+4x)

Expand

P(x) = 300-2x-5000 - 4x

Rearrange:

P(x) = -2x+300-4x  - 5000

P(x) = -6x- 4700

The profit function is P(x) = -6x-4700

For  the company to break even, R(x) = C(x)

300-2x = 5000+4x

300-5000 = 4x+2x

6x = -4700

x = -4700/6

x = -783 units

Note that the functions are assumed. Use this concept to solve your real question

Answer 2

If the profit function is P(x) = -6x-4700 then the units that must be produced to break even is 783 units.

Here, We can assume revenue and expenses.

Let R(x) = 300x - 2x²

C(x) = 5000 + 4x

How do you calculate revenue profit?

It is the difference between the total revenue and the total expenses.

Profit = Revenue - Cost

P(x) = R(x) - C(x)

P(x) = 300-2x - (5000+4x)

Expand

P(x) = 300-2x-5000 - 4x

P(x) = -2x + 300 - 4x  - 5000

P(x) = -6x- 4700

The profit function is P(x) = -6x-4700

For  the company to break even, R(x) = C(x)

300-2x = 5000+4x

300-5000 = 4x+2x

6x = -4700

x = -4700/6

x = -783 units

Therefore, we can calculate the profit function and break-even for the company of any value, if the profit function is P(x) = -6x-4700 then the units that must be produced to break even is 783 units.

Learn more about revenue profit here:

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