Assumptions of Linear Programming

1.    Conditions of Certainty.

It means that numbers in the objective and constraints are known with certainty and do change during the period being studied.
2.    Linearity or Proportionality.

We also assume that proportionality exits in the objective and constraints. This means that if production of 1 unit of product uses 6 hours, then making 10 units of that product uses 60 hours of the resources.

It means that total of all activities quails the sum of each individual activity. In other words there is no interaction among all the activities of the resources.

We make the divisibility assumption that solution need to be in whole numbers (integers). Instead, they are divisible and may take any fractional value, if product cannot be produced in fraction, and integer programming problem exists.

In LP problems we assume that all answers or variables are non-negative. Negative values of physical quantities are an impossible situation. You simply cannot produce a negative number of cloth, furniture, computers etc.

An optimal solution cannot compute in the situation where there is infinite number of alternative activities and resources restriction.

In linear programming problems of maximum profit solution or minimum cots solution always occurs at a corner point of the set of the feasible solution.

8. Agricultural goods have to be transported from sources S₁, S₂ and S₃ to destinations D₁, D₂ and D₃. The transportation cost per unit, capacities of the sources and requirements of the destinations are given in the following table:

	D1	D2	D3	Supply
S1	8	5	6	120
S2	15	10	12	80
S3	3	9	10	80
Demand	140	80	50

1. 
   Using the a. North-West Corner (NWC) Method, Least Cost Method (LCM), and Vogel’s Approximation (or penalty) Method (VAM, obtain the initial basic feasible solution,.
   
2. 
   Formulate it as a Linear Programming Problem.
   

Using North -West Corner Method, the non- degenerate initial basic feasible solution is given in Table 1.