Here's an example of what I was talking about. You could use hundreds of constraints and variables if you wanted to, but to keep it simple I'll just use a few, and avoid sticky widgets like amortizing cost for equipment or multi-period inventory management, although you can include all of those and more in a more detailed analysis. This is an incredibly powerful tool for analyzing business decisions, and will give you an optimal solution, as well as identify the range in which the answer remains optimal if costs or demands change.

Let's say you run a 3bbl British brewpub.

You have $5000 cash at the beginning of the week in your beer budget.

You need at least 20 kegs of beer, but you never need more than 60 kegs per week.

The costs of brewing your beer, how much you sell it for per pint, and profit per keg:

mild - $40 / $3 / $320

stout - $50 / 4 / 430

IPA - $60 / 4 / 420

barley-wine - $90 / 5 / 510

The costs of beer you can buy

bitter for $70 / 3 / 290

ESB for $80 / 4 / 400

porter for $90 / 4 / 390

foreign stout for $100 / 5 / 500

(There are 120 pints per keg.)

No more than 1/4 of your sales volume will be from $5 pints, at least 1/3 of your sales volume will be from $3 pints.

You want to maximize profit:

Max: 320m + 430s + 420i + 510bw + 290b + 400e + 390p + 500fs

subject to the following constraints:

1) 40m + 50s + 60i + 90bw + 70b + 80e + 90p + 100fs <= $5000

2) m + s + i + bw + b + e + p + fs >= 20

3) m + s + i + bw + b + e + p + fs <= 60

4) (bw + fs) <= 0.25(m + s + i + bw + b + e + p + fs)

= 0.75bw + 0.75fs - 0.25m - 0.25s - 0.25i - 0.25b - 0.25e - 0.25p <= 0

5) (m + b) >= 0.33(m + s + i + bw + b + e + p + fs)

= 0.67m + 0.67b - 0.33s - 0.33i - 0.33i - 0.33bw - 0.33e - 0.33p - 0.33fs >= 0

The results tell us that the optimal solution is $24822 profit, from 20 kegs of mild, 25 kegs of stout, and 15 kegs of barleywine. It also tells you that for every keg of IPA you add, the profit decreases by $46. For every keg of bitter or esb, it'll decrease by $30, for porter $40, and for foreign stout $10.