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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 hae egatie aiales so eee to state estitios

▪ 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

• Constraints:

o Stain Remover: %1 PM > = %3

▪ Meas that you eed 3 pited edia to ahiee 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 Alays ilude this i all uestios 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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