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Homework Help: Modelling question

  1. Mar 2, 2006 #1
    Hi a few questions i want to check my answers for here,

    3. Write down an expression, evaluate the constant of proportionality, and answer the question.
    [Remember to work in SI units. Simplify answers to 1 d.p. only.]
    (a) The annual cost (C) of running a business is partly constant and partly proportional to the number of employees.
    If there are 20 employees, the annual cost is $400000.
    If there are 25 employees, the annual cost is $470000.
    Find the annual cost if there are 18 employees

    What is meant by partly constant? how would this be written.

    C = kN? or C = kN + c?
  2. jcsd
  3. Mar 2, 2006 #2
    The second one since I guess you mean a constant by c. The first one is as you can see "fully" proportional.
  4. Mar 4, 2006 #3
    hrmk so finished that question and was hoping for some help on this next one.

    In a bookstore, the selling price of a certain dictionary is $x. The total profit ($P) on the sale of the dictionary is partly proportional to the selling price of the dictionary and partly proportional to the square of the selling price of the dictionary. When x = 35, P = 78750; when x = 60, P = 60000.
    (a) Express P in term of x.
    (b) Find the total profit if the selling price of the dictionary is $65.

    For a) im not certain but this is my expression,

    P = ( kx ) + (x^2) + c
    P = x(k + x) + c

    with my values of c = 107100 and k = -845 found from info given..

    so when x = 65 P = 65(-845+65) + 107100
    P = $56400

    cheers, any corrections and pointers would be great.
    Last edited: Mar 4, 2006
  5. Mar 4, 2006 #4
    It doesn't say partly constant, so why is 'c' in the equation? With a nonzero 'c' in your equation, you would have a profit even if the selling price is zero. No, think about it again. What should the equation be?
  6. Mar 5, 2006 #5
    ahah woops, my bad..

    So in that case it will be

    P = x . x^2
    P = Kx^3

    However when i solve for k the answers are different..
    Last edited: Mar 5, 2006
  7. Mar 5, 2006 #6


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    I find the phrasing "partly proportional to the selling price and partly proportional to the square of the selling price" confusing but I'm sure "P= k x (x2)= x3" is not intended since that would simply be "proportional to the cube of the selling price". You were closer with your first idea: P= kx+ (x2)+ c. As Assyrian_77 said, drop the c since nothing is said about a constant- and remember that "proportional to the square of the selling price is "cx2". You don't have a constant of proportionality on the x2.
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