3.3 Graphing and Solving Systems of Linear and Absolute...
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3.3 Inequality Systems and 3.4 Linear Programming Part 1.notebook 1 September 15, 2017 3.3 Graphing and Solving Systems of Linear and Absolute Value Inequalities Objective: to solve systems of inequalities
Transcript of 3.3 Graphing and Solving Systems of Linear and Absolute...
3.3 Inequality Systems and 3.4 Linear Programming Part 1.notebook
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September 15, 2017
3.3 Graphing and Solving Systems of Linear and Absolute
Value Inequalities
Objective: to solve systems of inequalities
3.3 Inequality Systems and 3.4 Linear Programming Part 1.notebook
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Steps for GraphingGraph the lines and appropriate shading for each inequality on the same coordinate plane.
Lines are dotted or solid.
The final shaded area is the section where all the shadings overlap.
* Sometimes it helps to use a different colored pencil for each line and shaded region.
3.3 Inequality Systems and 3.4 Linear Programming Part 1.notebook
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Solve the system of inequalities by graphing.
3.3 Systems of Inequalities
x y > 2 2x + y < 5
1st inequality in y = mx + b form:
Shade
2nd inequality in y = mx + b form:
Shade
Answer is where the colors overlap!
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4) Solve the system of inequalities by graphing.
y 3y < –| x + 2| + 5
>
3.3 Inequality Systems and 3.4 Linear Programming Part 1.notebook
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ASSIGNMENT
HW 3.3p. 136 #5, 919 odd,
28, 31, 37,
4349 odd
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3.4 Linear ProgrammingPart I
3.3 Inequality Systems and 3.4 Linear Programming Part 1.notebook
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VOCABULARY
Linear Programming identifies conditions that make a quantity as large (maximum) or as small (minimum) as possible.
This quantity is expressed as the objective function.
Limitations are placed on the variable.
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TESTING VERTICESIf there is a max or min value of the objective function, it occurs at one or more vertices of the feasible region.
Vertices of Feasible Region
3.3 Inequality Systems and 3.4 Linear Programming Part 1.notebook
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Find the values of x and y that maximize the objective function of P = ‐x+3y.
Now test the vertices of the feasible region(2,8)
(2,0)
(5,0)
(5,2)Max of 22 at (2,8)
3.3 Inequality Systems and 3.4 Linear Programming Part 1.notebook
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Graph the system of constraints. Name all vertices.
Then find the values of x and y that maximize the objective function: C = 3x + y
Vertices of feasible region:
Max of ___ at ( __, __ )
3.3 Inequality Systems and 3.4 Linear Programming Part 1.notebook
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Graph each system of constraints. Name all vertices. Then find the values of x and y that minimize and maximinze the objective function:
P = 2x + 3y
Min of _____ at (__ , __)
Max of _____ at (__ , __ )
Vertices of feasible region:
3.3 Inequality Systems and 3.4 Linear Programming Part 1.notebook
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ASSIGNMENT
HW 3.4 p. 142 # 1‐7 odd and 18‐19
Rewrite #19 as x + y > 6
x + y < 13
x > 3, y > 1
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