This preview shows pages 1–7. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Algebraic Solution of LPPs  Simplex Method To solve an LPP algebraically, we first put it in the standard form . This means all decision variables are nonnegative and all constraints (other than the nonnegativity restrictions) are equations with nonnegative RHS. Converting inequalities into equations 2 1 3 2 x x z + = Subject to , 6 2 3 6 3 2 1 2 1 2 1 ≥ ≤ + ≤ + x x x x x x Maximize Consider the LPP We make the ≤ inequalities into equations by adding to each inequality a “slack” variable (which is nonnegative). Thus the given LPP can be written in the equivalent form 2 1 3 2 x x z + = Subject to , , , 6 2 3 6 3 2 1 2 1 2 2 1 1 2 1 ≥ = + + = + + s s x x s x x s x x are slack variables. 2 1 , s s Maximize Thus we seem to have complicated the problem by introducing two more variables; but then we shall see that this is easier to solve. This is one of the “beauties” in mathematical problem solving. The ≥ inequalities are made into equations by subtracting from each such inequality a “surplus” (nonnegative) variable. Thus the LPP 2 1 3 2 x x z + = Subject to , 2 2 3 6 3 2 1 2 1 2 1 ≥ ≥ + ≤ + x x x x x x Maximize is equivalent to the LPP 2 1 3 2 x x z + = Subject to , , , 2 2 3 6 3 2 1 2 1 2 2 1 1 2 1 ≥ =+ = + + s s x x s x x s x x is a slack variable; is a surplus variable....
View
Full
Document
This note was uploaded on 04/15/2011 for the course CSCI 528 taught by Professor Rashid during the Spring '11 term at George Mason.
 Spring '11
 Rashid

Click to edit the document details