Posted by Hannah on .
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?
from x+5y=5000, we get y=(5000-x)/5
substitute into f(x) to get:
Take derivative and equate to zero. I get x=2500,
find y using equation from 3)
did you get 1000-2x/5 as a derivative for x(5000-x)/5?
Yes, your derivative is correct.
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