Representation of simplex method, Managerial Accounting

Representation of Simplex method

We shall use the example previously stated for the graphical solution. The standard form of the model is given by:

Maximize :  Z = 3XE + 2X1 + OS1 + OS2 + OS3 + OS4
Subject to:  XE + 2XI + S1 = 6

2XE + XI + S2 = 8
-XE + XI + S3 = 1
XI + S4 = 2

XE, XI, S1, S2, S3, S4 ≥ 0

The figure depicts the solution space. Every point in this space can be represented in terms of the variables XE, XI, S1, S2, S3 and S4 of the standard form. (To show this point, observe that Si = 0, i = 1,2,3 and 4 turns the related equation into an edge of the solution space. For example: Si = 0 is equivalent to XE + 2XI = 6, which represents edge CD. Having S1 > 0 will move the feasible points from edges toward the interior of the solution space).

Our main interest is to identify the extreme points algebraically. When we examine the figure we note that the values of XE, X1, S1, S2, S3 and S4 associated with the extreme points A, B, C, D, E, and F have the following definite pattern with regard to whether or not their values are equal to zero.

        Extreme           Zero                Non-zero
        Point             Variables            Variables

        A                    XE, XI               S1, S2, S3, S4
        B                    S2, XI               S1, XE, S3, S4
        C                    S2, SI               X1, XE, S3, S4
        D                    S4, SI               X1, XE, S3, S2
        E                    S4, S3               X1, XE, S1, S2
        F                    S4, XE               X1, S3, S1, S2

Two observations are instantly obvious:

543_graph.jpg


Since the standard form has four equations and six unknowns, each extreme point must have two
 (= 6 - 4) variables at zero level.

 

Posted Date: 12/7/2012 6:31:25 AM | Location : United States







Related Discussions:- Representation of simplex method, Assignment Help, Ask Question on Representation of simplex method, Get Answer, Expert's Help, Representation of simplex method Discussions

Write discussion on Representation of simplex method
Your posts are moderated
Related Questions
dentify and explain the many classsification of cost for planning,control,performance evaluation and decision making

what are the most effective management styles in an organisation

Input or exogenous variables These are variables of two types: 1) Controlled variables: These are variables that can be controlled by management. By changing the input

Disadvantages of activity based costing 1) It is essentially not the panacea for all ills. 2) It absorbs a lot of resources. 3) Too much emphasis on customer viability c

MAKE OR BUY DECISIONS (NO LIMITING FACTORS) The choice between making and buying a given component is one which is likely to face all businesses at some time.  It is often one


Feed-forward control system Feed-forward control system describes a system in which deviations in the system are anticipated in a forecast of future results, so that corrective

Standard conventions in Game Theory Consider the following table as shown below: X plays row I, Y plays Column I, X wins 3 points X plays row I, Y plays Column II, X los

The Role of Computers in Simulation Computers can be used to: 1) To generate the random numbers 2) To simulate thousands of trials. This is done extremely fast, accuratel