Class Notes (809,390)
MGOC10H3 (34)
Vinh Quan (14)
Lecture

# Lecture - Sept 18.doc

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School
University of Toronto Scarborough
Department
Management (MGO)
Course
MGOC10H3
Professor
Vinh Quan
Semester
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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