1. optimisation problem

I'm really having difficulty with performing these.

The question asks "Find the two positive integers such that the sum of the first number and four time the second number is 1000 and the product of the number is as large as possible; Let the two number to be found a and b respectively and let f be their product. "
Last part of question reads "The maximum of which of the following function will provide a solution to the problem?"

I get as far as $1000 = a + 4b$, then I'm lost. I think I should have 2 functions and then need to put one in term of the other to create one function, but this is where I get lost.

2. Originally Posted by Craka
I'm really having difficulty with performing these.

The question asks "Find the two positive integers such that the sum of the first number and four time the second number is 1000 and the product of the number is as large as possible; Let the two number to be found a and b respectively and let f be their product. "
Last part of question reads "The maximum of which of the following function will provide a solution to the problem?"

I get as far as $1000 = a + 4b$, then I'm lost. I think I should have 2 functions and then need to put one in term of the other to create one function, but this is where I get lost.
yes. what about the product? you were told what to call that. that is the second equation you need