Math - Functions

The research department in a company that manufactures AM/FM clock radios established the following cost, and revenue functions:

R(x) = x(50-1.25x)
C(x) = 160 + 10x
where 0 < x < 20.

a) Determine when R = C (to the nearest thousand units. e.g. 6.247)
Quantity x = ________ thousand units.

b) Determine the maximum profit (to the nearest thousand dollars).
Profit P = _______ thosand dollars.

My answers don't seem to be correct (x = 16 and P = 160) Please help!

  1. 👍
  2. 👎
  3. 👁
  1. set R(x) = C(x)
    x(50-1.25x) = 160 + 10x
    50x - 1.25x^2 -160 - 10x = 0
    1.25x^2 -40x + 160 = 0
    x^2 - 32x + 128 = 0
    complete the square
    x^2 - 32x = -128
    x^2 - 32x + 256 = -128+256
    (x-16)^2 = 128
    x-16 = ±√128

    x = 16± √128 = 4.686 or 27.314 , but 0 < x < 20
    so x = 4.686

    I will assume your R, C, and P represent
    Revenue, Cost and Profit respectively, thus
    P(x) = x(50-1/25x) - (160 + 10x)
    = 50x - 1.25x^2 - 160 - 10x
    P'(x) = 50 - 2.5x - 10
    = 0 for a max of P
    2.5x = 60
    x = 24

    max profit = P(24) = ....
    I will let you push them buttons.

    1. 👍
    2. 👎
  2. Is max profit 80 than? I am plugging it back into P(x) = = 50x - 1.25x^2 - 160 - 10x right?

    1. 👍
    2. 👎
  3. yes!, good job

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    A company manufactures and sells x cellphones per week. The weekly price-demand and cost equations are given below P=400-.5x and C(x)=20000+130x What price should the company charge for the phones and how many phones should be

  2. 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

  3. statistics

    In a batch of 8,000 clock radios 5% are defective. A sample of 14 clock radios is randomly selected without replacement from the 8,000 and tested. The entire batch will be rejected if at least one of those tested is defective.

  4. accounting

    A company has an overhead application rate of 125% of direct labor costs. How much overhead would be allocated to a job if it required total direct labor cost of $20,000? $5,000. $16,000. $25,000. $125,000. $250,000. The R&R

  1. math

    A dealer bought some radios for a total of $1,200. She gave away 6 radios as gifts, sold each of the rest for $10 more than she paid for each radio, and broke even. How many radios did she buy?

  2. Stats

    5. The board of directors for Procter and Gamble is concerned that only 19.5% of the people who use toothpaste buy Crest toothpaste. A marketing director suggests that the company invest in a new marketing campaign which will

  3. math

    The PJC department of McIntyre Company shows gross sales of $730,600 for computer supplies and $934,900 for general office supplies. It has determined that computer supplies cost $534,000 and that general office supplies cost

  4. algebra

    You are an entrepreneur and selling handmade kites. Your company Kites-R-Fun has been contacted by a customer in Alaska who wants to purchase several of your best-selling kites and wants you to ship them to her. You have already

  1. linear programming

    The Pyrotec Company produces three electrical products-clocks, radios and toasters. These products have the following resources requirements : Resource Requirements Cost/Unit Labor Hours/Unit Clock $7 2 Radio 10 3 Toaster 5 2 The

  2. Calculus

    A company decides to begin making and selling computers. The price function is given as follows: p=−70x+4000, where x is the number of computers that can be sold at a price of p dollars per unit. Additionally, the financial

  3. Managerial Economic

    The ABC Company manufactures AM/FM clock radios and sells on average 3,000 units monthly at 25$ each to retail stores.Its closest competitor produces a similar type of radio that sells for 28$. a. If the demand for ABC's product

  4. History

    Why was the Dutch East India Company called a multinational corporation? 1 It was a Dutch company but only did business in Indian tea. 2 It was a Dutch company but was owned by monarchs of many European nations. 3 It was a Dutch

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