Math(Urgent)
posted by Hannah .
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.

objective function f(x)=xy
constraint: x+5y=5000 
For the same question:
3) Rewrite the objective function in terms of the variable x only.
I out x=50005y
4) For which value of x does the objective function attain its maximum?
Do I have to take the derivative?