Question

What is the difference between the assumption of linearity and continuity in LPP

The above question carry 10 marks. Please prepare a min of 600 Words answer sheet

Answer 1

A linear programming problem is the method derving the best possible outcome or solution from a given set of parameters or requirements, which are represented in the form of linear relationship, which forms one of the assumptions of a linear programming problem which is the linearity, Linearity is the basis of a linear programming problem.

The two important aspects of an LPP are the objective function and the contraints both are expressed as afucntion of the decision variables. The underlying condition is that the functions are to be linear means these functions are expressed as a proportional to the decision variables.Linearity alsoknown as proportionality refers to form a first degree equation. also the equations formed using the contraints and objective function can be represented as straight lines on a graph.In simple terms it can be explained as if the cost of producing one unit of item X1 is Rs 5/- then 10 units should cost rs 50/- only  Also the lienarity requires that effect of the value os each variable on the values of objective function and the constrains are additive means he there is no overlapping between the effects of different activities , The level of activity X1 should not affect the cost or benefit associated with the level of activity of another acivity X2.or we can say the the variables are to be independent.

Another important assumption of a LPP is the continuity, by continuity we mean the dicsion variable can take not only the integet values but fractional values This means that the combinatins of outputs can be interpreted as a combination of fractional as well as integer values of decision variables. Suppose we have got a soution of 19/3 items of product X1 and 23/3 items of X2 are to be produced in a week , either the 1/3 or 2/3 part of the product can be taken as work inporgress and can be accounted as a complete product in the next week, or else we can interpret the result as 17 items of X1 and 23 items of X2 in 3 weeks.

So summarising the above facts we can say that continuity makes the decision variable to take any fractional values while linearity confirms that the relation is linear and the the variables are independent .