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    Linear Programming Objectives: 1.) to be able to find FEASIBLE SOLUTIONS and analyze for the optimal solutions. 2.) to understand optimal solutions and how they maximize or minimize a real life model. 3.) to Effectively solve linear system of inequalities manually and using excel.

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    Linear Programming Objectives: 1.) to be able to find FEASIBLE SOLUTIONS and analyze for the optimal solutions. 2.) to understand optimal solutions and how they maximize or minimize a real life model. 3.) to Effectively solve linear system of inequalities manually and using excel.

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    194 views12 pages

    Linear Programming

    Uploaded by

    msbakermath
    Linear Programming Objectives: 1.) to be able to find FEASIBLE SOLUTIONS and analyze for the optimal solutions. 2.) to understand optimal solutions and how they maximize or minimize a real life model. 3.) to Effectively solve linear system of inequalities manually and using excel.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PPTX, PDF, TXT or read online from Scribd
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    of 12

    Chapter 7.

    5 Linear Programming
    Objectives: 1.) To be able to find feasible solutions and analyze for the optimal solutions 2.) To understand optimal solutions and how they maximize or minimize a real life model 3.) Effectively solve linear system of inequalities manually and using Excel

    Goal: Consider the problem


    A farmer has two crops planted by the acre: wheat (X) and corn (Y). Say it is calculated that each acre of wheat takes 3 hours of labor and 2 pounds of fertilizer. Corn is calculated that each acre takes 2 hours of labor and 4 pounds of fertilizer. Wheat brings in $200 of profit/acre and corn brings in $300 per/acre. If the farmer has 45 acres of land, 100 hours of labor available, and 120 lbs of fertilizer, find the number of acres to plant of each crop in order to maximize the profit.

    Vocabulary
    Optimization: A process in which you are asked to find the minimum or maximum of a quantity
    Example: Find the advertizing routes that would minimize cost for marketing Example: Find the number of acres to plant particular crops to maximize profit

    Objective Function: a linear equation that represents the equation you want to minimize or maximize Constraints: A system of linear inequalities that represents the situation

    Manual Linear Programming


    1.) Pick your variables and KNOW what they stand for. 2.) Determine your objective function 3.) Determine your constraints 4.) Graph your constraints (they form a system of linear inequalities) 5.) Find the vertices of the region (These are your FEASIBLE SOLUTIONS) 6.) Plug the feasible solutions into your objective function. Pick out the maximum/minimum value

    Example

    Example: Start on 34

    Homework: 7.5
    Pg 529 #2-3; 8; 34-37

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