Answered

Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

You are currently evaluating your business and trying to decide how much you need to sell to make a profit. Choose one of the following options for your cost and revenue functions. The variable, x, represents the number of units sold.
c(x)=300+260x
r(x)=300x-xsquared

For the option you chose, find the value(s) of x (the number of units sold) to break-even. Show all your work by typing it in or uploading a picture of your handwritten work. What is your profit function, P(x)? What is your profit when you sell 10 more than a break-even point? Is that what you expected? Show all your work

Sagot :

From the given functions, of the cost, c(x) = 300 + 260•x, and revenue, r(x) = 300•x - x², we have;

First part;

The values of x to break-even are;

x = 30, or x = 10

Second part;

The profit function, P(x) is presented as follows;

P(x) = x•(40 - x) - 300

Third part;

  • The profit (loss) when 10 more units is sold than the break-even point, x = 30 is -($300) unexpected

  • The profit when 10 more units is sold than the break-even point, x = 10 is $100

How can the given functions be used to find the profit made?

The cost is c(x) = 300 + 260•x

Revenue is r(x) = 300•x - x²

First part;

At the break even point, we have;

  • c(x) = r(x)

Which gives;

300 + 260•x = 300•x - x²

x² + 260•x - 300•x + 300 = 0

  • x² - 40•x + 300 = 0

Factoring the above quadratic equation gives;

x² - 40•x + 300 = (x - 30)•(x - 10) = 0

At the break even point, x = 30, or x = 10

The values of x at the break even point are;

  • x = 30 units sold
  • x = 10 units sold

Second part;

Profit = Revenue - Cost

The profit function, P(x), is therefore;

P(x) = r(x) - c(x)

Which gives;

P(x) = (300•x - x²) - (300 + 260•x)

P(x) = 300•x - x² - 300 - 260•x

P(x) = 300•x - 260•x - x² - 300

P(x) = 40•x - x² - 300

The profit function is therefore;

  • P(x) = x•(40 - x) - 300

Third part;

When 10 more units are sold than the break even point, we have;

x = 30 + 10 = 40 or x = 10 + 10 = 20

The profit at x = 40 or x = 20 are;

P(40) = 40•(40 - 40) - 300 = -300

  • P(40) = -($300)

When the number of units sold, x = 40, the profit is, P(40) = -($300) unexpected loss

  • The profit (loss) when the number of units sold increases to 40, of -($300) is unexpected.

At x = 20, we have;

P(20) = 20•(40 - 20) - 300 = 100

  • P(20) = $100

  • When the number of units sold, x = 20, the profit is, P(20) = $100

Learn more about functions here:

https://brainly.com/question/88581

#SPJ1

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.