the profit of a company, in dollars, is the difference between the company's revenue and cost. the cost C(x), and R(x) are functions for a particular company. the x represents the number of items produced and sold to distributors. C(x)=2000+60x R(x)=860x-x^2
Determine the maximum profit of the coming.

  1. 👍
  2. 👎
  3. 👁
  1. p = R - C = -x^2 + 800 x - 2000
    dp/dx = -2x + 800 = 0 at max or min
    so x = 400 at max or min of p
    is it a max or a min
    well if x is large - or +, the sides of the parabola zoom negative so the vertex was a max (if you do not know calculus complete the square to find vertex of that parabola)
    p = -160,000 + 800(400) - 2000
    = -160, 000 + 320,000 - 2,000

    1. 👍
    2. 👎
  2. how do you find dp/dx?

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra

    The total profit function,​ P(x), for a company producing x thousand units is given by P(x)=−2x^2+38x−120. Find the values of x for which the company makes a profit. [Hint: The company makes a profit when P(x)>0.] Explain

  2. Math - Limits/Derivatives

    Suppose that for a company manufacturing calculators, the cost, revenue, and profit equations are given by C = 70,000 + 20x R = 300x - (x^2 / 20) P = R - C where production output in 1 week is x calculators. If production is

  3. math

    the profit (p), in dollars, for a company is modeled by the function p(x) = -750x^2 + 15,000x, where x is the number of items produced. For which values of x will the company lose money?

  4. calculus

    A manufacturing company sells high quality jackets through a chain of specialty shops. the demand equation for this jackets is p = 400 − 50q where p is the selling price ( in dollars per jacket) and q is the demand ( in

  1. Algebra

    A print shop makes bumper stickers for election campaigns. If x stickers are ordered (where x < 10,000), then the price per sticker is 0.28 − 0.000002x dollars, and the total cost of producing the order is 0.087x − 0.0000005x2

  2. math

    A printing company determines that to print a large format poster, it costs $75 to set up the production process. Each poster that is printed costs $22 in material and labor. The printing company sells these posters to marketing

  3. precal

    A cell phone company’s profit is modeled by the function p(x) = 10x − x2 − 1, where p is expressed in thousands of dollars and x is the number of phones sold in hundreds. How many phones must the company sell to make a

  4. economics

    2. A company is considering building a bridge across a river. The bridge would cost $2 million to build and nothing to maintain. The following table shows the company¡¯s anticipated demand over the lifetime of the bridge: Price

  1. Math

    A company’s profit is described by the equation P(x) = – 5x^2 + 300x + 15,000 where x is the price in dollars that the company charges for its product. What should the company charge for the product to generate the maximum

  2. algebra

    The total cost (in dollars) for a company to manufacture and sell x items per week is C=50x+40 whereas the revenue brought in by selling all x items is R=68x−0.3x^2. How many items must be sold to obtain a weekly profit of $200?

  3. math

    PLEASE HELP!!! This is a last minute homework help!!! A computer software company models the profit on its latest video game using the relation: p(x) = -4x^2+20x-9, where x is the number of games produced in hundred thousands and

  4. analazye profit functions

    For a certain company, the cost function for producing x items is C(x)=40x+150 and the revenue function for selling x items is R(x)=−0.5(x−80)2+3,200. The maximum capacity of the company is 100 items. The profit function P(x)

You can view more similar questions or ask a new question.