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    cnycole's Avatar
    cnycole Posts: 6, Reputation: 1
    New Member
     
    #1

    Jan 28, 2011, 12:32 PM
    A problem that doesn't make sense- a linear cost function
    Please help me, I am getting only negative answers that I think are absolutely wrong. This problem has five parts:

    Jill starts a business of manufacturing custom seat cushions for large trucks. She determines that the fixed cost is $1,375 and unit cost is $22. She sells each cushion for $49.95.

    A) Find the linear cost function C(x), revenue function R(x) and profit function P(x) assuming x cushion were made and sold.
    ---for this I was able to make these functions. Please correct me if I'm wrong:

    --->C(x)= 49.95x+1375; R(x)= 22x; P(x)=22x-49.95x+1375

    B) Find the cost, revenue, and profit if 200 cushions were made and sold.

    ---> My answers: Cost is $11,365; Revenue is $4,400; and Profit is $-6,965

    C) How many cushions must she make and sell in order to attain a profit of $5,000?

    ---> This is where I find a problem, because using the P(x)=R(x)-C(x)gives me a negative answer.

    D) Find the break-even

    E) Graph C(x) and R(x)
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member
     
    #2

    Jan 28, 2011, 12:57 PM


    You have the incorrect Revenue function.

    The Cost function is:



    The Revenue function is:



    The Profit is:



    For a profit of 5000, then



    cushions

    And so on

    Break even is when R=C.

    So,

    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #3

    Jan 28, 2011, 12:58 PM

    C(x) is wrong and should be

    C(x) = 1375 + 22x

    Then, R(x) becomes:

    R(x) = 49.95x

    And profit:

    P(x) = 49.95x - (1375 + 22x)

    Can you try again now? :)

    EDIT: A minute difference galactus :p
    cnycole's Avatar
    cnycole Posts: 6, Reputation: 1
    New Member
     
    #4

    Jan 30, 2011, 02:41 PM
    Comment on Unknown008's post
    Thank you so much!
    cnycole's Avatar
    cnycole Posts: 6, Reputation: 1
    New Member
     
    #5

    Jan 30, 2011, 02:41 PM
    Comment on galactus's post
    Thank you!!

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