MAth

posted by .

Pat Kan owns a factory that manufactures souvenir key chains. Her weekly profit (in hundreds of dollars) is given by P(x)=-2x^2+60x-120, where x is the number of cases of key chains sold.

a) what is the largest number of cases she can sell and still make a point?

b) Explain how it is possible for her to lose money if she sells more cases than your answer in part (a)

I've been doing this problem since lastnite and i couldn;t figure out the answer. someone help me please? ireally need to learn how to solve this kind of problem. midterm is coming :[

  • MAth -

    I don't know what level of math you are taking, is it Calculus?
    if you find the vertex (by Calculus or completing the square), you should have had (15, 330)
    which means that if she sells 15 cases she makes a maximum profit of 330.

    Your function is a parabola which opens downwards, so any other value besides x=15 would produce a smaller value than 330

    this parabola crosses the x-axis at appr. 2.1 and 27.8
    so it is positive for number of cases between 3 and 27 cases.
    For any other number of cases, P(x) would be negative.

    e.g. let x = 30 cases
    P(30) = -120

  • MAth -

    thanks for the help really appreciate it! im taking business math. anyway, how did you find out that the parabola crosses the x-axis at appro. 2.1 and 27.8? and how did you come up with 27 cases?
    sorry for asking a lotta questions. i just want to understand this problem.

    Thanks again

  • MAth -

    Sorry about not answering last night, but had gone to bed.

    I solved
    0 = -2x^2+60x-120 using the quadratic formula

    since x has to be a whole number, 3 and 27 would be the first and last whole numbers for which the parabola is above the x-axis, that is , for which P is positive.
    Try subbing in x = 28 and x = 2, you will get a negative value for P.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calc

    A widget factory has fixed costs of 35 billion dollars and variable costs of 781 million dollars per widget. The revenue (in $ billions) from selling x number of widgets is given by the following for x between 0 and 60. R(x) = 0.11(60x …
  2. Calc

    Demand is q=-p^2+33p+9 copies of a book sold per week when price is p dollars. Can you help determine what price the company should charge to get the largest revenue?
  3. math

    when using a calculator to find the square root of a number, which of the following is the correct sequence of steps?
  4. Business Math

    Lee Corp. purchased 10 key chains on January 1, 2010 for $9.00 each and 5 key chains were purchased on December 1, 2010 for $10.00. Seven were sold. What would be the inventory amount for LIFO, what would be the inventory amount for …
  5. math

    A company's weekly profit, in riyals, is modeled by the function P(u)=-0.032u^2+46u-3000. where u is the number of units sold each week. a) the maximum weekly profit b) the loss for week's holiday period, where no units are sold c) …
  6. algebra. help!

    1. 3x+10≥4 a. x≥-2 b. x≤ 2 c. x≤-2 d. x≥ 2 ** 2. The tennis team is selling key chains as a fundraiser. If its goal is to raise at least $180, how many key chains must it sell at $2.25 each to meet that …
  7. Calculus

    The marginal profit in dollars on Brie cheese sold at a cheese store is given by P'(x)=x(60x^2+30x), where x is the amount of cheese sold in hundreds of pounds. The "profit" is -$50 when cheese is sold. a. Find the profit function. …
  8. Algebra 2

    Can someone please help me do the follow problem... ...The cost (in dollars) of producing x sneakers in a factory is given by c(x)=60x+750. The number of sneakers produced in (t) hours is given by x(t)=50t. Fund c(x(t)). Evaluate c(x(5)) …
  9. Easy Maths Question

    A manufacturer of souvenir items makes key rings which sell for $5.80 each. The cost of manufacturing is $1250 to set up the process, and then $0.80 per key ring. 1) Write a rule for the income in dollars, S, from selling n of these …
  10. Maths

    A manufacturer of souvenir items makes key rings which sell for $5.80 each. The cost of manufacturing is $1250 to set up the process, and then $0.80 per key ring. 1) Write a rule for the income in dollars, S, from selling n of these …

More Similar Questions