$ x ≥ 0$,
$ y ≥ 0$,
$2x + y < 8$
$x + 2y < 10$
Does x + y have a maximum value under the above conditions?
How I tried to do it:
I knew that x and y are positive numbers, and if trying to find the maximum value, they are most likely positive numbers.
I solve the system of inequalities 2x + y < 8, nd x + 2y < 10, to find possible values of x and y.
I get $ 2 < x$, and $y < 4$.
After plugging in those values for x and y respectively, I find that one of the inequalities gives an answer that does not satisfy the inequality.
$2x + y < 8$,
$2(2) + (4) = 8$
RHS must be greater than LHS, therefore that is not the case.
In order to satisfy the inequality, one number must be less than the other by 1. That means the maximum sum of the values x and y is equal to 5.
I have no idea if I'm right, and if this is the 'proper' way to do it so to speak, so guidance, other ideas, etc. would be really helpful. Tips on approaching minimum/maximum problems would be cool too. I'm just starting out in this kind of stuff.