# Linear programming

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Topic :- Linear Programming The running of any firm or of a factory involves many constraints like financial,space,resources,power etc. The objective of any business person would be to make the profit maximum (in the case of investment to make the cost a minimum) under all the constraints.The linear programming problem is the problem of optimising an objective function under a given set of constraints.When the objective function is profit function the optimisation is to maximise the profit.In the case of cost function the optimisation is to minimise the cost. All the constaints of the problem are linear inequalities and the objective function is linear.Hence, it is called LPP.The following are a few illustrations of the LPP by Graphical method . 1. Maximise : P = Subject to : . ≤ 20 ≤6 0. Now we draw the graphs of the equations feasible region. = 20, and = 6 and recognise the Y A(0,6) B(8,6) =600 C(10,5) O(0,0) D(15,0) X The shaded region OABCDO (bounded) represents the feasible region in which all the Constraints of the problem are satisfied. Now, we evaluate the objective function at these corners of the region. Vertex 0 0 0 0 A 0 6 3X0+5X6=30 B 8 6 3X8+5X6=54 C 10 5 3X10+5X5=55 D 15 0 3X15+5X0=45 From the above table we observe that Maximum value of P is 55 and corresponds to X = 10 and y = 5 2). Minimise: C = Subject to : ≥ 6 4. ≥ 6 . we draw the graphs of the linear equations Y B(1,3 ) D( ) O C(3,1 ) X The shaded reg ...
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