Essential Ingredients of Linear Programming
Formulation of suitable mathematical model to explain the given situation is the starting point of linear programming. The model can be conveniently framed by getting the answer to the following queries :
i) What factors or values are not known ?
ii) What is the objective ?
iii) What are the restrictions, specifications or constraints ?
This information is then translated into the following ingredients of Linear Programming. All linear problems have four properties in common:
- Objective function
The function to be optimized is known as objective function. It is some sort of linear mathematical relationship between the variables/factors under consideration. The major objective of a typical firm is to maximize profits in the long run. In the case of a trucking or airline distribution system, the objective might be to minimize shipping costs.
2. Constraints or Restrictions
The constraints limits the degree to which we can pursue our objective. These are the set of restrictions imposed on the variables or some combination of few or all the variables appearing in the objective function. These constraints or restrictions are due to limitations of manpower, capacity of plant, capital available or time constraints etc. For example, deciding how many units of each product in a firm’s product line to manufacture is restricted by available labor and machinery. We want, therefore, to maximize or minimize a quantity(the objective function) subject to limited resources(the constraints).
3. Feasible Solutions
A feasible solution o linear programming problem is a set of values for the variables X1,X2,….. Xn which simultaneously satisfies all the constraints. For a given problem there can be many feasible solutions depending on the nature of the phenomenon.
4. Optimal Solution
A feasible solution, which optimizes the objective function, is known as optimal solution. An optimal solution is always feasible but all feasible solutions cannot be optimal.