MB0048 Q1. a. What do you mean by linear programming problem? Explain the steps involved in linear programming problem formulation?

Answer: The LPP is a class of mathematical programming where the functions representing the objectives and the constraints are linear. Optimisation refers to the maximisation or minimisation of the objective functions.

You can define the general linear programming model as follows:

Maximise or Minimise:

Z = c1 x1 + c2 x2 + - - - - + cn xn

Subject to the constraints,

a11 x1 + a12 x2 + ----- + a1n xn ~ b1

a21 x1 + a22 x2 + ----- + a2n xn ~ b2

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am1 x1 + am2 x2 + ------- + amn xn ~ bm

and x1 ≥ 0, x2 ≥ 0, -------------------- xn ≥ 0

Where cj, bi and aij (i = 1, 2, 3, ….. m, j = 1, 2, 3 ------- n) are constants determined from the technology of the problem and xj (j = 1, 2, 3 ---- n) are the decision variables. Here ~ is either ≤ (less than), ≥ (greater than) or = (equal). Note that, in terms of the above formulation the coefficients cj, bi aij are interpreted physically as follows. If bi is the available amount of resources i, where aij is the amount of resource i that must be allocated to each unit of activity j, the “worth” per unit of activity is equal to cj.