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by: Vivien Bradtke V


Vivien Bradtke V
Texas A&M
GPA 3.6


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This 1 page Class Notes was uploaded by Vivien Bradtke V on Wednesday October 21, 2015. The Class Notes belongs to MATH 141 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 35 views. For similar materials see /class/226046/math-141-texas-a-m-university in Mathematics (M) at Texas A&M University.

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Date Created: 10/21/15
Math 141 WIR Spring 2007 Benjamin Aurispa Math 141 Key Topics 3133 Section 31 Graphing Inequalities o For each inequality7 replace the inequality sign with an equal sign and graph the line Use a dashed line if the inequaility is lt or gt Use a solid line if the inequality is S or 2 0 Pick a test point in one of the regions and plug it into the inequality to see if it makes the inequality true If it makes the inequality TRUE7 then this region IS part of the solution If it makes the inequality FALSE7 then this region is NOT part of the solution 0 The solution set to a system of inequalities is the region that makes every inequality TRUE7 called the feasible region or feasible set Shade this region as required Some instructors want you to shade the true region7 other instructors want you to shade the false region called reverse shading Be aware of what your instructor requires In all cases7 label the feasible region 0 A solution set is bounded if it can be enclosed by a circle Otherwise7 it is unbounded Sections 32 33 o A linear programming problem consists of the following First7 dont forget to DEFINE YOUR VARIABLES 1 objective functioniwhat you are trying to maximize or minimize 2 constraintsiusually in the form of inequalities These are recognized by key words such as at least7 at most7 no more than77 etc o If the feasible region is bounded7 there is both a maximum and a minimum 0 If the feasible region is unbounded7 there will usually be a minimum but no maximum Note the word usually This may not always be true In the unbounded case7 you need to consider the objective function 0 To solve a linear programming problem7 use the method of corners 1 Graph the feasible region or set 2 Find all corner points vertices 3 Evaluate the objective function at every corner point 4 Two cases assuming there is a maximimminimum If the objective function is maximizedminimized at exactly one corner point7 then this point is a unique solution 7 If the objective function is maximizedminimized at two adjacent corner points7 there are in nitely many solutions These solutions all lie on the line segment joining the two corner points 0 Leftover resources are the differences between how much you actually use and how much was available


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