Lecture2eve

# Lecture2eve - MBAC6080 Decision Modeling and Applications...

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1 MBAC6080 Thomas Vossen Assistant professor of Operations Management Leeds School of Business University of Colorado Boulder, CO 80309-0419 Decision Modeling and Applications

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Lecture 2, 1-23-2008 2 MBAC6080 Today’s Agenda Intro to Linear Programming Models (LPs) The Graphical Method for solving LPs LP Concepts Examples of LPs
Lecture 2, 1-23-2008 3 MBAC6080 Introduction We all face decision about how to use limited resources such as: Oil in the earth Land for dumps Time Money Workers

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Lecture 2, 1-23-2008 4 MBAC6080 Mathematical Programming. .. MP is a field of management science that finds the optimal, or most efficient, way of using limited resources to achieve the objectives of an individual or a business. a.k.a. Optimization
Lecture 2, 1-23-2008 5 MBAC6080 Elements of LP Models Decision variables What we want to decide? Objective function How we will decide? Constraints What binds our decision? Quantities: How much/many to produce/buy/hire/etc . Specified as Linear Functions

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Lecture 2, 1-23-2008 6 MBAC6080 Formulating LPs
Lecture 2, 1-23-2008 7 MBAC6080 Blue Ridge Hot Tubs produces two types of hot There are 200 pumps, 1566 hours of labor, and 2880 feet of tubing available. Aqua-Spa Hydro-Lux Pumps 1 1 Labor 9 hours 6 hours Tubing 12 feet 16 feet Unit Profit \$350 \$300 Example

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Lecture 2, 1-23-2008 8 MBAC6080 Example Step 1: Specify decisions X 1 = “Number of Aqua-Spas to produce” X 2 = “Number of Hydro-Luxes to produce”
Lecture 2, 1-23-2008 9 MBAC6080 Example Step 2: Specify Objective Maximize Profits: Maximize 350X 1 + 300X 2

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Lecture 2, 1-23-2008 10 MBAC6080 Example Step 3: Specify constraints (restrictions) Pump Availability 1X 1 + 1X 2 ≤ 200 Labor Hours Availability 9X 1 + 6X 2 ≤ 1566 Tubing Availability 12X 1 + 16X 2 ≤ 2880
Lecture 2, 1-23-2008 11 MBAC6080 Example Step 4: Identify any upper or lower bounds on the decision variables. X 1 ≥ 0 X 2 ≥ 0

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Lecture 2, 1-23-2008 12 MBAC6080 Linear Programming Model Maximize 350X 1 + 300X 2 Subject to 1X 1 + 1X 2 ≤ 200 9X 1 + 6X 2 ≤ 1566 12X 1 + 16X 2 ≤ 2880 X 1 , X 2 ≥ 0 Ingredients: Objective function Constraints Decision Variables
13 MBAC6080 Another LP Example A farmer is preparing to plant a crop in the spring and needs to  fertilize a field.  There are two brands of fertilizer he can use:   SuperGro and CropKwik.  Each brand has a specific amount of  nitrogen and phosphate.  The field requires at least 16 pounds  of nitrogen and 24 pounds of phosphate.  SuperGro costs \$6  per bag and CropKwik \$3.  How many bags of each type should  the farmer use to adequately fertilize his field? (lbs / bag)

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Lecture2eve - MBAC6080 Decision Modeling and Applications...

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