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Lecture 1

BU275 Lecture Notes - Lecture 1: Feasible RegionPremium

1 pages73 viewsWinter 2018

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Monday January 8th 2018
Lecture 1
Linear Programming
Make simultaneous decisions to reach an optimal output by considering constraining
factors (ex. Limited resources)
o Example: Optimization problems
Can only have addition or subtraction signs between decision variables in the
objective function and the constraints in linear programming (LP)
o Ex. 4T + 2C < 10
Objective is to maximize or minimize something
Non-negativity constraints
o Ca’t hae egatie aiales so eee to state estitios
Ex. T > or = 0, C > or = 0
Linear Programming: Graphical Solution
Plot all objective functions
Check corner points
Optimal mix = last point you touched in feasible region
The Profit & Gambit Co.
An advertising campaign will focus on 3 key products: stain remover, liquid detergent
and powder detergent
Decision Variables: #TV #PM
Objective: $1 TV + $2 PM
o Minimizes
o Stain Remover: %1 PM > = %3
Meas that you eed 3 pited edia to ahiee this goal, does’t atte
how many TV ads you run
Graphical solution: Draw PM = 3 (Area above that horizontal line is the
feasible region)
o Liquid: %3 TV + %2 PM > = %18
o Powder: -%1 TV + %4 PM > = %4
Non-Negativity Constraints: TV > = 0, PM > = 0
o Alays ilude this i all uestios o else it’s ot alid
Finding Optimal Solution
Find corner points
Plug those into the objective function
Optimal solution is the lowest number
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