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) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit!

Answers to some of the questions are given below so that you can check your work.

Assuming that the company sells all that it produces, what is the profit function?
Preview Change entry mode .

Hint: Profit = Revenue - Cost as we examined in Discussion 3.

What is the domain of P(x)?
Hint: Does calculating P(x) make sense when x=−10 or x=1,000?

The company can choose to produce either 40 or 50 items. What is their profit for each case, and which level of production should they choose?
Profit when producing 40 items =

Profit when producing 50 items =

Can you explain, from our model, why the company makes less profit when producing 10 more units?

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    The revenue from selling q items is R(q) = 600q − q^2, and the total cost is C(q) = 150 + 50q. Write a function that gives the total profit earned. It is my understanding that profit = revenue - costs. So when I tried to write

  2. pre-calculus

    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.

  3. Calculus

    A company manufactures x units of one item and y units of another. The total cost in dollars, C, of producing these two items is approximated by the function C=7x^2+xy+1y^2+600. A) If the production quota for the total number of

  4. Calculus

    The marginal cost for producing x units of a certain product is given by the formula MC = 0.001x^2-0.5x+66.5. A. What is the increase in the cost of the production if the production level is raised from 200 to 400 units? B. What

  1. Business calc

    A total revenue function is given by R(x) = 1000(x^2 - 0.1x)^1/2 , where R(x) is the total revenue, in thousands of dollars, from the sale of x items. Find the rate at which total revenue is changing when 20 items have been sold.

  2. Math

    2. The cost of producing x units of a certain commodity is given by Px  1000  0 x MCsds, where P is in dollars and Mx is marginal cost in dollars per unit. A. Suppose the marginal cost at a production level of 500 units is

  3. college algebra

    At Allied electronics, production has begun on x-15 computer chip. The total revenue function is given by. R(x)=47x-0.3x^2 and the total cost function is given C(x)=8x+16, where x represents the number of boxes of computer chip

  4. 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?

  1. math

    A manufacturing company finds that the daily cost of producing x items of a product is given by c(x)=210x + 7000. Find x using calculus

  2. Math

    The total cost (in dollars) for a company to manufacture and sell x items per week is C(x)=70x+400. If the revenue brought in by selling all x items is R(x)=90x−0.05x^2, find the weekly profit. How much profit will be made by

  3. Math

    The cost (in dollars) of producing x air conditioners is C=g(x)=560+40x. Find a formula for the inverse function g−1(C).

  4. Mathematics

    Suppose that the selling price P of an item for the quantity X sold is given by the function P=-1/3x+44 Express the revenue R as a function of x (R=x*p ) how many items must be sold to Mackenzie the revenue and what is the maximum

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