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University of Toronto Scarborough

Management (MGO)

MGOC10H3

Vinh Quan

Fall

Description

MGTC74 Analysis for Decision Making
Lecture 02
Chapter 2 – Solving LP Model – Graphical Method & Sensitivity Analysis of Constraints
LPterminology
Example – Giapetto’s problem
MAX Z = 3X + 2X1 2
S.T. 2X + X ≤ 100 (finishing)
1 2
X 1 X ≤ 20 (carpentry)
X 1 40 (soldier demand)
X 1 0 , X ≥20
• Any specification of values for variables is called a solution eg. X = 10, X = 102
• Feasible solution is a solution that satisfies all constraints and sign restrictions
eg. [X 1 40, X =220] or [X = 31.5, X = 202001] or …
• The feasible region is set of all feasible solutions.
• Given many feasible solutions, goal is to find the best or optimal solution.
• For max problem, optimal (best) solution is one which maximizes value of objective.
• For min problem, it is one which minimizes objective.
• Solutions which are intersection of 2 or more constraints are called corner feasible solutions (at corner of
feasible region). The optimal solution for an LP must be a corner feasible solution.
• LPs can have one optimal solution, multiple optimal solutions, or problem can be infeasible (no
feasible solution) or unbounded ( Z = ∞ or Z = - ∞)
Slack
Given optimal solution, can compute the slack for any “≤” constraints. Slack = right hand side – left hand side.
Optimal solution for Giapetto, X * 1 20, X * =260
• For X 1 X ≤ 20 hrs, Slack = 80 – (X * + X1*) = 82 – (20 + 60) = 0.
• For X 1 40 u

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