Adjacent extreme points, Managerial Accounting

Adjacent extreme points differ in only one variable

The first observation indicates that we can identify the extreme points of the solution space algebraically by setting zero as many variables as the difference between the number of unknowns and the number of equations. This is a unique property of the extreme points.

The unique property of the extreme points yields the following general procedure for determining the extreme points algebraically. Assume that the standard form has m equations and n variables (m ≤ n) together with the non-negativity restrictions. All the feasible extreme points are determined by considering all the unique non-negative solutions of the m equations in which exactly n - m variables are set equal to zero.

Mathematically, the unique solutions resulting from setting n - m variables equal to zero are called basic solutions. If a basic solution satisfies the non-negativity restrictions, it is called a feasible basic solution. The variables set equal to zero are called non basic variables; the remaining ones are called basic variables.

The general conclusion is that the algebraic definition of basic solutions in the simplex method now takes the place of the extreme point in the graphical solution space.

The second of the two observations is very useful computationally because the simplex method moves from a current extreme point to an adjacent one.  Since adjacent extreme points differ only in one variable we can determine the next (adjacent) extreme point by interchanging a current non basic (zero) variable with a current basic valuable. This idea greatly simplifies the simplex method computations.

The basic-non basic interchange process gives rise to two suggestive names. The entering variable is a current non basic variable that will "enter" the set of basic variables at the next (adjacent extreme point) iteration. The leaving variable is a current basic variable that will "leave" the basic solution in the next iteration.

Posted Date: 12/7/2012 6:37:41 AM | Location : United States







Related Discussions:- Adjacent extreme points, Assignment Help, Ask Question on Adjacent extreme points, Get Answer, Expert's Help, Adjacent extreme points Discussions

Write discussion on Adjacent extreme points
Your posts are moderated
Related Questions
Ask question #MRead ALL instructions before getting started! ABC Corporation is a new company that buys and sells office supplies. Business began on January 1, 2014. Given on th

h. Production orders that had cost 450,000 to complete according to their job cost sheets were shipped to customers during the month. These goods were sold on account at 50% above

Decision-making is an integral part of all management functions. It is the process of choosing the among alternative courses of action. Managers have to

Issa Company manufactures a personal computer designed for use in schools and markets it under its own label. Issa has the capacity to produce 25000 units a year but is currently p

Comparing real and planned outcomes and responding to Divergences from Plan The final phases in the process outlined in figure shown below of comparing real and planned outcome

A manufacturing  company  needs  2500 units  of a particular component every  year. The  company buys  it at the rate of Rs. 30 per  unit.  The order processing cost for this part

Question: (a) "Budgetary control comprises two distinct elements - Planning and Control''. ‘'A budget is a statement of what it is reasonable to believe can be made to ha

differentiate between multiple product, selling product and margin managent


define budget control system