The other time, I was talking about a man that owns a mug factory ,I said in order for the man to maximize his profit, he has to make use of linear program modeling, that is, he has to model the problem as a linear program modeling.

There are four basic steps of linear program modeling and they are listed below

• Identify and label the decision variables

• Determine the objective and use the decision variables to write an expression for the objective function as a non geometric function of the decision variables

• Determine the explicit constraints and write an expression for each of them as a linear equation/inequality in the decision variables

• Determine the implicit constraints and write them as a linear equation/inequality in the decision variables

DECISION VARIABLES

I can say knowing the decision variables is the most difficult part of linear program modeling To get the right variables, it is advisable to put yourself in the shoe of the decision maker ,then ask yourself what you can do to your job.
Actually, in the real world, there is a modeler that follows the decision maker around for a certain period of time recording all actions and decisions the decision maker must make

In the process of modeling, it is very essential to resist assumptions or in the process of modeling, do not assume about the nature of the solution.

The last point here would not be over emphasized because the experienced modelers also fall in to this trap, since it is sometime difficult to overcome the temptation of assumption. Again in order for the man to maximize his profit, he has to take the four steps listed above

Like the example I gave the last time I discussed linear programming, the man that owns a plastic mugs industry and he want to maximize his profit. They produce designed mugs. The profit on a case of mug is $25. The mugs are manufactured with a machine called the plastic extruder which feeds on plastic resins. Each case of mugs requires 20Ibs. Per case. The daily supply of plastic resins is limited to at most 1800 pounds. About 15 cases of the product can be produced per hour. At the moment the man wants to limit their work day to 8 hours, let approach this using the steps listed above

Let B be the number of mugs produced daily.
B =NUMBER OF MUGS PRODUCED DAILY
MAXIMIZE PROFIT: PROFIT = REVENUE –COSTS
PROFIT =25B
RESIN USED: 20B ≤1800
LABOR: B/15 ≤ 8
IMPLICIT CONSTRAINTS:
THE DECISION VARIABLES ARE POSITVE: 0≤B
MAXIMIZEDPROFIT =25B
SUBJECT TO 20B ≤1800
1/15B ≤8
0 ≤B

Like I said earlier that the first step in the modeling process, identification of the decision variables, is always the most complex or difficult

Never be panic to join more decision variables either to clarify the model or to improve its flexibility. Modern linear program software easily solves problems with thousands of variables on a laptop, or even tens of millions of variables on specialized hardware and networks. It is more essential to get an accurate, easily interpretable, and a non rigid model in order to provide a compact model, my next publish will be on problem associated with the input data for real world linear programs.