Question 999941
Let the two numbers be x and y.
Assume x is larger than y.
The sum would be {{{x+y=60}}}
So then {{{y=60-x}}}
So the product of the two numbers is,
{{{P[1]=x*y=x(60-x)}}}
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The difference of 60 would be,
{{{x-y=60}}} 
{{{y=x-60}}}
So the product of the two numbers is,
{{{P[2]=x*y=x(x-60)}}}
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Yes, you can set up a problem however you want. 
Sometimes it won't make sense. 
Example: Make a shape using 40' of wire so that the enclosed shape has the minimum area. You could just make a straight line of 4 lengths of 10' of wire so that the enclosed area is zero. 
Well if you're a farmer and you want to make a pen, 
why would you want the minimum area, 
you'd want the maximum area for your animals to graze.