Some terms of Linear Programming you must understand before you begin

In my previous blog, I was a bit cautions in not giving you a big bout of some Latin and French type of taxonomy of Linear Programming and restrained myself in focusing only on giving you some basic understanding in most layman kind of way on what is Linear Programming. Since, you have already understood what Linear Programming is, we shall gradually understand various terms associated with it.

The first and core word is “Optimization”. All LPPs are optimization problems as either we minimize the cost or maximize the profit under given constraints. Thus optimization is maximization of profit or minimization of loss or cost. See this example,

A cooperative society of farmers has 50 hectares of land to grow two crops A and B. The profit from crop A and B per hectare are estimated as Rs. 10500 and Rs. 9000 respectively. To control weeds, a liquid herbicide has to be used for crops A and B at rate of 20 liters and 10 liters per hectare respectively. Further, no more than 800 liters of herbicide should be used in order to protect fish and wildlife using a pond which collects drainage from this land. How much land should be allocated to each crop to maximize the total profit of the society?

Thus this is an optimization problem which maximizes the profit under the given conditions. Thus, if x hectare of land is allocated to crop A, and y hectare of land is allocated to crop B, the given constraints are:

1. x ≥ 0; y ≥ 0.

2. x + y ≤ 50; and, 20x + 10y ≤ 800 or x + 5y ≤ 400

Then, we have to maximize z = 10500x + 9000y

Now this equation z = 10500x + 9000y, which is of the form of Max or Min Z = ax + by, where a and b are constants, is called “Objective Function”.

The variables x and y in the objective function are called “Decision Variables”.

Another term “Constraints”, you are already aware of from the preceding two examples, are inequalities framed on decision variables translating the given restrictions into a linear form.

Some more important terms will be introduced to you after I give you a brief sketch of how to solve these questions using graph and two-dimensional geometry. The first and core word is “Feasible Region”.