# 331-04 - T, C > (nonnegativity) Text pp. 49-59, 2-1.xls...

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Special Situations in LP 1. Redundant Constraints - do not affect the feasible region Example: x < 10 x < 12 The second constraint is redundant because it is less restrictive.

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Special Situations in LP 1. Infeasibility – when no feasible solution exists (i.e., there is no feasible region) Example: x < 10 x > 15
Special Situations in LP 1. Alternate Optimal Solutions – when there is more than one optimal solution Max 2T + 2C subject to: T + C < 10 T < 5 C < 6 T, C > 0 0 5 10 T C 10 6 0 2T + 2C = 20 All points on green line segment are optimal

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Special Situations in LP 1. Unbounded Solutions – when nothing prevents the solution from becoming infinitely large Max 2T + 2C Subject to: 2T + 3C > 6 T, C > 0 0 1 2 3 T C 2 1 0 Direction of solution
Using Excel Solver for LP Recall the Flair Furniture Example: Max 7T + 5C (profit) subject to the constraints: 3T + 4C < 2400 (carpentry hours) 2T + 1C < 1000 (painting hours) C < 450 (max number of chairs) T > 100 (min number of tables)

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Unformatted text preview: T, C > (nonnegativity) Text pp. 49-59, 2-1.xls Designing the Spreadsheet • Note the separation & clear labeling of key data: Variables ( = Changing Cells), Objective Function (= Target Cell), and Constraints, formatted as LHS and RHS • The sign cell between the LHS and RHS is not used in any way, it is informational • Constraints can be organized in any sequence, but it is best to put similar ones together. (Why?) Problem 2.18 • Note that the constraints can be set up in different ways. Do you see any of these? Summary • 4 assumptions of LP should be satisfied • Graphical and Algebraic methods are a solution technique for 2-varible LP • Excel Solver can solve some practical size LP • More professional software for solving LP is available (LINDO, LINDO, CPLEX, XPRESS)...
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## This note was uploaded on 08/29/2011 for the course ACCT 331 taught by Professor A during the Spring '11 term at Ohio State.

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331-04 - T, C > (nonnegativity) Text pp. 49-59, 2-1.xls...

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