Posted by **Hannah** on Sunday, February 27, 2011 at 10:07pm.

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) -
**MathMate**, Sunday, February 27, 2011 at 10:26pm
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) -
**Hannah**, Sunday, February 27, 2011 at 10:54pm
Thank You

- Math(Urgent) -
**Hannah**, Sunday, February 27, 2011 at 11:19pm
did you get 1000-2x/5 as a derivative for x(5000-x)/5?

- Math(Urgent) -
**Helper**, Sunday, February 27, 2011 at 11:30pm
Yes, your derivative is correct.

- Math(Urgent) -
**khalifa**, Saturday, March 16, 2013 at 11:53am
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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