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March 27, 2017

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Compute the maximum product for two positive numbers x and y with the property that the sum of the first plus five times the second is 5000.

1) Indicate the objective equation
2) Indicate the constraint equation

So the objective = f(x)=xy and the constraint = x+5y=5000

Now number 3 says rewrite the objective function in terms of the variable x only. Would it be y=x?

4) For which value of x does the objective function attain its maximum? Do I have to take the derivative?

5) What is the corresponding value of y
6) What is the vale of the maximum product of the two numbers?

  • Math(Urgent) - ,

    3)
    from x+5y=5000, we get y=(5000-x)/5
    substitute into f(x) to get:
    f(x)=xy=x(5000-x)/5

    4)
    Take derivative and equate to zero. I get x=2500,

    5)
    find y using equation from 3)

    6)
    x*y

  • Math(Urgent) - ,

    Thank You

  • Math(Urgent) - ,

    did you get 1000-2x/5 as a derivative for x(5000-x)/5?

  • Math(Urgent) - ,

    Yes, your derivative is correct.

  • Math(Urgent) - ,

    The financial officer for an accounting firm allows Dh 50,000 for computer supplies in the annual budget. After 6 months, Dh 26,200 has been spent on supplies. Is this figure within 55% of the annual budget?

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