It’s just a means of solving problems when there are apparently too many variables to otherwise make sense of the situation with a simple algebraic solution. The problem needn’t be complex, it only needs to have many options. For example…

You need to buy some filing cabinets. You know that Cabinet X costs $10 per unit, requires six square feet of floor space, and holds eight cubic feet of files. Cabinet Y costs $20 per unit, requires eight square feet of floor space, and holds twelve cubic feet of files. You have been given $140 for this purchase, though you don’t have to spend that much. The office has room for no more than 72 square feet of cabinets. How many of which model should you buy, in order to maximize storage volume?

For the solution and how to set up the problem, see the site:
http://www.purplemath.com/modules/linprog3.htm

Linear programming works with an objective function and constraint functions. The objective function is just some multi-value function that you want to maximize or minimize. Cost is frequently used.

The constraints are just linear functions that the variables need to satisfy. Once you have that idea down, then the examples links that you have been given should make sense.