After some more research, I discovered that this was an integer programming problem, so the simplex algorithm by itself cannot solve it; something more general like a backtracking algorithm must be used instead, apparently. For anybody who stumbles across this thread in the future, here are some materials that could shed some light on these kinds of problems.

Oh, actually, I'm just trying to work the algorithm out on problems by hand to see if I understand it, so I don't have any code. I'm not asking for any, either; I plan to write some as soon as I get this algorithm down. My issue is that when dealing with standard optimization problems in linear programming using the simplex method I'm just not sure what to do with non-integer answers when the problem requires integers (like having 1 human as compared to 1.5 humans). For instance, here is a problem I found online:

Given:
100x + 125y + 50z <= 500
50y + 100z <= 400
and x, y, z are non-negative integers.
Maximize 10x + 20y + 15z.

After running through the simplex algorithm, the answer I obtained was 97.5 for the max, y = 3, and z = 2.5. However, the real answer is 95; I think that's because x, y, and z are integers, whereas my z is a decimal. If I round my solution to (0, 3, 2) my new maximum is 90, so apparently I have to do something other than rounding. (I know 97.5 is correct for the decimal answer because I checked using a simplex calculator here). Even if on the off chance that 95 was actually the wrong answer for this particular problem, what should I do with my decimal quantities/maximums if the next problem I see only asks for integers?