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Lecture

# Lecture - Sept 11.doc

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University of Toronto Scarborough

Management (MGO)

MGOC10H3

Vinh Quan

Fall

Description

MGTC74 Analysis for Decision Making
Lecture 01
Chapter 2 – LP Model Formulation & Solution
Basic components of linear programming (LP) model:
1) Define decision variables—variables that describes the decisions to be made
2) State objective function—in LP model decision maker will want to maximize (e.g., profit,
output, revenue) or minimize (cost, risk) some function of decision variables
3) Specify constraints
4) Sign restrictions or variables—in general we can have x≥0, x≤0, x unrestricted in sign
• if x1,x2must be integer, then we have an integer programming problem
2
• if either objective function or any of the constraints is nonlinear e.g., 3x + 21 then w2 have
nonlinear programming problem
Example – Production Planning
1) x =1# of soldiers to make each week
x = # of trains to make each week
2
2) objective is to maximize profits
Profit = (27x +121x ) –2(10x + 91 +14x 2 10x 1 = 3x +22x 1 2
3) constraint 1 no more than 100 hrs finishing time used
finish time soldier + finish time trains ≤ 100hr 2x + 1x 1100 2
constraint 2 no more than 80hrs carpentry time used
1x 1 1x ≤82
constraint 3 at most 40 soldiers can be sold
x 1 40
4) cannot produce negative # of soldiers/trains so x ,x > 1 2
Final LP model
Max z = 3x 1 2x 2
2x1+ 1x ≤200 (finishing)
1x1+ 1x ≤20 (carpentry)
x1< 40 (soldier demand)
x , x > 0
1 2
1 Example – Production Planning
For every gallon A

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