Limitations of linear programming simplex method

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Limitations of linear programming simplex method

Mathematically it applies to those problems which require the solution of maximisation problems subject to a system of linear inequalities stated in terms of certain variables. If and b, the two variables are the function of c, the value of c is maximised when any movement from that point results in a decreased value of c.

The value of c is minimised when even a small movement results in an increased value of c. An illustration could explain us the model of linear programming.

Limitations of linear programming simplex method

Let us consider a linear programming problem and solve it by algebraic method. An important thing that has to be understood is to ascertain the given problem as linear programming, is to write the objective function and the constraints in the form of equations or inequalities.

Illustration 1 Presume an industry manufactures two commodities M1 and M2.

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The manufacture of these commodities requires inputs X, Y and Z and their available volume are 14, 10 and 4 relatively. Assumed that the manufacture of one commodity M1 procures 2 units of input X, 1 unit of input Y and does not require input Z and the manufacture of one unit of commodity M2 requires 2 units of input X, 2 units of Y and 4 units of Z.

Derivate the above problem into linear programming and solve it with algebraic method. Solution First we shall convert the above write-up as linear equations in order to determine solution. This is represented in the below diagram which could give us a graphical solution to the equation.

There are three J, K, P and Y corner points or intense points of this possible area. The intense point J is ascertained by only one constraint of input Z and according to it 4 units of commodity M2 and no amount of M1 are produced.

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Substituting this in profit function we get profits at intense point J. As will be noted from the possible area, according to the intense point K, 4 units of commodity M2 are manufactured. The productivity of two commodities at intense point be got by solving the constraints equation of input X and Y.

With these productivities of M1 and M2 profits are:In mathematical optimization, the revised simplex method is a variant of George Dantzig's simplex method for linear programming. The revised simplex method is mathematically equivalent to the standard simplex method but differs in implementation.

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A number of steps have to be adopted to proceed in a systematic manner before one can arrive at the solution. 3. Graphic solution method has lot of applications and is relatively short and simple. However, it has limitations and cannot be applied to problems with more than two variables in the objective function.

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Limitations of linear programming simplex method

the simplex method: minimization In Section , we applied the simplex method only to linear programming problems in standard form where the objective function was to be maximized. Linear Programming Linear programming is often a favorite topic for both professors and students.

The ability to introduce LP using a graphical approach, the relative ease of the solution method, the widespread availability of LP software packages, and the wide range of applications make LP accessible even to students with relatively weak .

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