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
-------------------------------------------
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.
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