Very often we have to solve the problems in a set constraints. If there are no constraint the solution is very easy. Similarly, the problem arises when we have to reach certain objectives and without that no problem exists. So most frequently occurring situations is to solve a problem to attain certain objective under certain constraints. The usual objective to the problem is to maximize or minimize. That is to maximize profitless of the conquer or lo minimize the cost/inventory etc. In linear programming, we will consider only one objective of the sort either maximize or minimize. If we have more one objective, it is indirectly dealt with the set of constraints. Otherwise we have to deal with the problems Multiple Criteria Decision Making (MCDM) which is an advanced technique.
In linear programming winch is shortly called as LP we require the objective function and the constraints as linear. By linear we means that any change in the values of the mathematical variables result in a proportional value in the outcome.
If we express tl~r: objective and the constraints in mathematical function, we will get the power of the function in first degree only. There is no variable or product of the variables in second degree alt above. Thus, there is no part of the constraints and the objective as x1^2.,x1x2 etc. of that form.
The set constructions can be related as equality (=), greater than or equal to (2) or less than or equal to (2). For example, a company may like to utilize the full manpower. This can be written as follows :
Manpower requirement = Manpower available.
The machine hour required for production should be less than what is available within the company. This can be written as follows :
Machine hour required <= Machine hour available.
The number of units for a particular product should exceed certain amount as it has already committed to a customer. This can he written as follows :
No. of units of a specified product L The company's commitment to the customer.
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