#Operations Research_OR
#Math_Statistics
#Linear Programming
#Formulation of LPP
A company manufactures daily 1,200 units at Factory-I and another 1,000 units at Factory-II. The daily demands at the three sales points are of 1,000; 700 and 500 units respectively. The shipping/transportation cost (Rs. per unit) are as follows:
Factory Sales Point – 1 Sales Point – 2 Sales Point – 3
I 14 13 11
II 13 13 12
Formulate this problem as an LP model to determine a minimum cost shipping/transport schedule for satisfying all daily demands.
General Mathematical Model of LPP:
The number of problems, showing how to model them by the appropriate choice of decision variables, objective, and constraints. Any linear programming problem involving more than two variables may be expressed as follows:
Find the values of the variable x1, x2,…………, xn which maximize (or minimize) the objective function
Z = c1x1 + c2x2 + ………….. + cnxn
subject to the constraints
a11x1 + a12x2 + …………. + a1nxn ≤ b1
a21x1 + a22x2 + …………. + a2nxn ≤ b2
……………………
am1x1 + am2x2 + ………….. + amnxn ≤ bm
and meet the non negative restrictions
x1, x2, …, xn ≥ 0
a) A set of values x1, x2,.. xn which satisfies the constraints of linear programming problem is called its solution.
b) Any solution to a linear programming problem which satisfies the non negativity restrictions of the problem is called its feasible solution.
c) Any feasible solution which maximizes(or minimizes) the objective function of the linear programming problem is called its optimal solution
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