Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion MATH 105: Finite Mathematics 3-1: The Inverse of a Matrix Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006
Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion Outline Introduction to Linear Programming 1 Systems of Linear Inequalities 2 Regions in the Plane 3 Conclusion 4
Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion Outline Introduction to Linear Programming 1 Systems of Linear Inequalities 2 Regions in the Plane 3 Conclusion 4
Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion Systems of Linear Equations In the last few sections, we have solving systems of linear equations . In doing this, we’ve been answering questions like: Sample Questions: 1 How do we use up exactly 45 lemons and 30 oranges? 2 How many days should cog factory A, B, and C run to produce exactly 550 basic, 725 standard, and 480 deluxe cogs? 3 How many servings of chicken, potatoes, and spinach should be served to yield 30 calories from carbs, 25 from protein, and 15 from fat?
Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion Systems of Linear Equations In the last few sections, we have solving systems of linear equations . In doing this, we’ve been answering questions like: Sample Questions: 1 How do we use up exactly 45 lemons and 30 oranges? 2 How many days should cog factory A, B, and C run to produce exactly 550 basic, 725 standard, and 480 deluxe cogs? 3 How many servings of chicken, potatoes, and spinach should be served to yield 30 calories from carbs, 25 from protein, and 15 from fat?
Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion Systems of Linear Equations In the last few sections, we have solving systems of linear equations . In doing this, we’ve been answering questions like: Sample Questions: 1 How do we use up exactly 45 lemons and 30 oranges? 2 How many days should cog factory A, B, and C run to produce exactly 550 basic, 725 standard, and 480 deluxe cogs? 3 How many servings of chicken, potatoes, and spinach should be served to yield 30 calories from carbs, 25 from protein, and 15 from fat?
Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion Systems of Linear Equations In the last few sections, we have solving systems of linear equations . In doing this, we’ve been answering questions like: Sample Questions: 1 How do we use up exactly 45 lemons and 30 oranges? 2 How many days should cog factory A, B, and C run to produce exactly 550 basic, 725 standard, and 480 deluxe cogs? 3 How many servings of chicken, potatoes, and spinach should be served to yield 30 calories from carbs, 25 from protein, and 15 from fat?
Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion Systems of Linear Equations In the last few sections, we have solving systems of linear equations . In doing this, we’ve been answering questions like: Sample Questions: 1 How do we use up exactly 45 lemons and 30 oranges? 2 How many days should cog factory A, B, and C run to produce exactly 550 basic, 725 standard, and 480 deluxe cogs? 3 How many servings of chicken, potatoes, and spinach should be served to yield 30 calories from carbs, 25 from protein, and 15 from fat?
Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion Systems of Linear Equations In the last few sections, we have solving systems of linear equations . In doing this, we’ve been answering questions like: Sample Questions: 1 How do we use up exactly 45 lemons and 30 oranges? 2 How many days should cog factory A, B, and C run to produce exactly 550 basic, 725 standard, and 480 deluxe cogs? 3 How many servings of chicken, potatoes, and spinach should be served to yield 30 calories from carbs, 25 from protein, and 15 from fat? In each of these cases, we are focusing on finding a unique solution which uses up or produces exactly a given amount of resources. Is this realistic?
Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion Linear Programming Consider making tart and sweet drinks from lemons and oranges. Suppose that the sweet drinks sold for more than the tart drinks. How many batches of each type of drink would we want to make? Example There are several approaches you could take: 1 Make only sweet drink since it sells for more. 2 Make only whichever type of drink you can make the most of. 3 Try to find the best way to divide up our fruit between both sweet and tart to make as much money as possible.
Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion Linear Programming Consider making tart and sweet drinks from lemons and oranges. Suppose that the sweet drinks sold for more than the tart drinks. How many batches of each type of drink would we want to make? Example There are several approaches you could take: 1 Make only sweet drink since it sells for more. 2 Make only whichever type of drink you can make the most of. 3 Try to find the best way to divide up our fruit between both sweet and tart to make as much money as possible.
Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion Linear Programming Consider making tart and sweet drinks from lemons and oranges. Suppose that the sweet drinks sold for more than the tart drinks. How many batches of each type of drink would we want to make? Example There are several approaches you could take: 1 Make only sweet drink since it sells for more. 2 Make only whichever type of drink you can make the most of. 3 Try to find the best way to divide up our fruit between both sweet and tart to make as much money as possible.
Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion Linear Programming Consider making tart and sweet drinks from lemons and oranges. Suppose that the sweet drinks sold for more than the tart drinks. How many batches of each type of drink would we want to make? Example There are several approaches you could take: 1 Make only sweet drink since it sells for more. 2 Make only whichever type of drink you can make the most of. 3 Try to find the best way to divide up our fruit between both sweet and tart to make as much money as possible.
Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion Linear Programming Consider making tart and sweet drinks from lemons and oranges. Suppose that the sweet drinks sold for more than the tart drinks. How many batches of each type of drink would we want to make? Example There are several approaches you could take: 1 Make only sweet drink since it sells for more. 2 Make only whichever type of drink you can make the most of. 3 Try to find the best way to divide up our fruit between both sweet and tart to make as much money as possible.
Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion Linear Programming Consider making tart and sweet drinks from lemons and oranges. Suppose that the sweet drinks sold for more than the tart drinks. How many batches of each type of drink would we want to make? Example There are several approaches you could take: 1 Make only sweet drink since it sells for more. 2 Make only whichever type of drink you can make the most of. 3 Try to find the best way to divide up our fruit between both sweet and tart to make as much money as possible. Trying to find the distribution of resources which makes us the most profit (or the lest cost) is called linear programming (when the re- strictions are linear expressions).
Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion Solving Linear Programming Problems Solving a linear programming problem involves finding and using two types of information. Parts of a Linear Programming Problem The two parts of a linear programming problem are: 1 Objective Function : The number to be maximized or minimized. 2 Constraints : Limits on a resource or other part of the problem.
Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion Solving Linear Programming Problems Solving a linear programming problem involves finding and using two types of information. Parts of a Linear Programming Problem The two parts of a linear programming problem are: 1 Objective Function : The number to be maximized or minimized. 2 Constraints : Limits on a resource or other part of the problem.
Introduction to Linear Programming Systems of Linear Inequalities Regions in the Plane Conclusion Solving Linear Programming Problems Solving a linear programming problem involves finding and using two types of information. Parts of a Linear Programming Problem The two parts of a linear programming problem are: 1 Objective Function : The number to be maximized or minimized. 2 Constraints : Limits on a resource or other part of the problem.
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