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Math Help - Help with Functions (I hope this is the right section!)

  1. #1
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    Help with Functions (I hope this is the right section!)

    EDIT: DUMB. I just saw the "Pre-Algebra and Algebra" section included functions. Sorry!

    Hi! I'm a grade 11 student preparing for my winter exams, and I've come across two questions that I can't seem to solve. Any help would be greatly appreciated.

    1) A small company produces and sells x widgets per week. They find that their cost function in dollars is C(x)=$50+3x and their revenue function in dollars is R(x)=6x-(x^2/100). How many widgets per week should be produced for maximum profits?

    I attempted to do 6x-(x^2/100)=$50+3x, then got (x^2/100)+3x-50=0 and used the quadratic equation. I got the wrong answer, so I'm assuming I made a no-no in making the two functions equal each other. What are you supposed to do, if you don't mind explaining?

    The second one is more confusing.

    2)A rectangular field is to be enclosed by a fence. Two fences, parallel to one side of the field, divide the field into three rectangular fields. If 2400 m of fence are available, find the dimensions giving the maximum area.

    I don't really understand how to get the answer here. Am I supposed to find the dimensions for the maximum area of the field?

    Thank you!
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  2. #2
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    Profit=Revenue-Cost, this is something that you just are supposed to know, even though it might not technically be a "math" topic

    So for this problem profit =R(x)-C(x)=6x-\frac{x^2}{100}-(50+3x)

    Now can you find the maximum? You will not set profit equal to 0 and solve with the quadratic formula because that will tell you when profit=0 and not the max profit. Instead you should know a rule about the max/min of a parabola in terms of the coefficients a,b of a quadratic equation

    Do you know this rule?
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  3. #3
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    Aha! Got it, thank you very much! That profit thing totally slipped my mind. I'll have to remember that because my teacher said there would be similar questions on the exam.

    Thanks, you were a big help.
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