Question

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

I put x+5y=5000. Is this correct.

Answer 1

objective function f(x)=xy
constraint: x+5y=5000

Answer 2

For the same question:

3) Rewrite the objective function in terms of the variable x only.

I out x=5000-5y

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