Posts

Simple method

Image
Problems 1.Use Simplex Method to solve Max Z = x1 + x2 + 3x3 Subject to the constraints 3x1 + 2x2 + x3 ≤ 3 2x1 + x2 +2x3 ≤ 2 And x1, x2, x3 ≥ 0 Solution: The standard form is Max Z = x1 + x2 + 3x3 + 0.S1 + 0.S2 Subject to the constraints 3x1 + 2x2 + x3 + S1 = 3 2x1 + x2 +2x3 +S2 = 2 And x1, x2, x3, S1, S2 ≥ 0 As all the net evaluation, Zj – Cj are non negative, an optimum solution has been reached. Hence  an optimum solution of the given L.P.P x1 = 0, x2 = 0 and x3 = 1 Max Z = 3  2.Use simplex Method to solve Max Z = 5x1 + 3x2 Subject to the constraints x1 + x2 ≤ 2 5x1 + 2x2 ≤ 10 3x1 + 8x2 ≤ 12 And x1, x2, ≥ 0 Solution: The standard form is Max Z = 5x1 + 3x2 + 0.S1 + 0.S2 + 0.x5 Subject to the constraints x1 + x2 + S1 = 2 5x1 +2x2 +S2 = 10 3x1 + 8x2 + S3 = 12 And x1, x2, S1, S2 , S3 ≥ 0 Solution: The standard form is  Max Z = 5x1 + 3x2 + 0.S1 + 0.S2 + 0.x5 Subject to the constraints  x1 + x2 + S1 = 2 5x1 +2x2 +S2 = 10 3x1 + 8x2 + S3 = 12 And x1, x2...
Read more

SIMPLEX METHOD

Meaning:      The Simplex method is an approach to solving linear programming models by hand using slack variables, tableaus, and pivot variables as a means to finding the optimal solution of an optimization problem.   Importance of the Simplex Method: Efficiency: It can effectively solve large-scale, complex linear programming problems, providing quick and accurate results. Versatility: Various fields make use of the Simplex Method, including finance, engineering, and business operations. Decision-making: It provides a rational and systematic approach for effective decision-making in various scenarios. Benefits of Simplex Method: The Simplex Method offers a range of benefits in problem-solving: Efficiency: It is highly efficient for solving linear programming problems, making it particularly attractive for large-scale applications with multiple variables and constraints. Flexibility: The method is highly adaptable and can be used for both maximisation and minimisati...
Read more

Stastics

                        Stastics  “Statistics are measurement, enumerations or estimates of natural or social phenomena, usually systematically arranged, analysed and presented as to exhibit Important inter- relationships among them.”                -A.M.Tuttle  Characteristics:  1. Statistics is a Quantitative Science: It does not deal with qualities. It deals only with quantities like mean mark, the correlation coefficient between expenditure on advertisement and sales, etc. Even while determining the association between two attributes , those qualities are to be expressed only in number such as the number of literates, the number of persons employed, etc.  2.It never considers a single item: Only a set of items is considered and a single item is never considered. A physician consider the mark of a student in one subject alone.  3.The valu...
Read more