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Chapter 6 Review: Linear Inequalities Textbook

321322, p348 Practice Questions p323, p.

Systems of Inequalities, Set Notation, Objective

number less than 3: )( A number greater than 2: ( >

equal to 7: x Anumberbetween0and5: X A number less

number: >c Graphing Linear Inequalities SLJ1L3

(fr STEP #2 Graph using slope + yintercept 5/ope j

1 Chapter 6 Review: Linear Inequalities Textbook p Summary: p , p348 Practice Questions p323, p Key Concepts: Graphing Linear Inequalities, Systems of Inequalities, Set Notation, Objective Function, Optimization Inequalities Vocabulary A number less than 3: )( A number greater than 2: ( > Anumbernotlargerthan5: A number greater than or equal to 7: x Anumberbetween0and5: X A number less than 5 or greater than 10: 5> x : C> A positive number: >c Graphing Linear Inequalities SLJ1L3 Graph x+2y<4 STEP#1Solvefory7?(fr STEP #2 Graph using slope + yintercept 5/ope j y iifr2 STEP #3 Test Point STEP #4 Shade fr 4//. ( > fi z : /. /..1, I I z: :: / :: :::::::: :::: I / / / Graphing a System of Linear Inequalities x0 1 Graph: y<x+4 : : : y < 2x +4 c, e re eic. I ::::::::: z : : : :: : / ZI11i11_ I, I (1 / I

2 Set Notation ((x,y)iy> 2x+ 1,x e R,y er) TheJof all (x,y) coordinates t y > 2x + 1 xis an I of the i numbers andyis an of the numbers. Domain: All of the possible xvalues (left to right) Range: All of the possible yvalues (down to up) Types of Numbers: Intevr 2.65 Rcii Is IV/i WiL I iki? ppj5 Example Graph the solution for ((x,y)(2y + 4 3x,x E I,y e I) y D: R:. Optimization Vocabulary Constraint =!4eq/ 17 y ct Feasible Region 7:a 5,o ObjectiveFunction= 4i L:oA ( w/cvkve, Maximize/Minimize = j1kj 1L) hvci c Oc.fc4 n, Optimize= /{./4((fI S /ki 1fg

.. N.. Key Example A toy company manufactures two types of toy

Because the supply of materials is limited, no more than 40

However, the company can make 70 or more vehicles, in total, each

sportutility vehicles that could be made.

minimum and maximum costs, and what those costs will be.

3 .. N.. Key Example A toy company manufactures two types of toy vehicles: racing cars and sportutility vehicles. Because the supply of materials is limited, no more than 40 racing cars and 60 sportutility vehicles can be made each day. However, the company can make 70 or more vehicles, in total, each day. It costs $8 to make a racing car and $12 to make a sportutility vehicle. There are many possible combinations of racing cars and sportutility vehicles that could be made. The company wants to know what combinations will result in the minimum and maximum costs, and what those costs will be. STEP #1: Define Variables ((acq rç C STEP #2: Write Constraints ro STEP #3: Note Restrictions. (C *J4.... / yc) (5 6i/ STEP #4: Graph. İN.;(p.) STEP #5: Label Corners 6 i I I I I I I I I I I I P C) Lv 66 STEP #6: Objective Function STEP #7: Maximum/Minimum (3C),o) O M)4VM 3oSjvs?Vc (o ii) ( Lj1iZ() rj14o iç4 S1 L6r5 $VU

4 Chapter 6 Review: Inequalities Practice #1: Graph each of the following. a)f(x,y)iyx+3,x E R,ye R} b) f(x,y)i3y+ 6< 2x,x E I,yE I) I i 4 I 1 c)((x,y)y 3,x> 4,x e W,y E W} djf(x,y)y> 2x N 4,2y x+ 1,x E R,y e R} y H /7 y :1

Practice #2: A student council is ordering signs for the winter dance.

No more than 30 of each size are wanted.

75 each, and postersize signs cost $14.50 each.

Let p represent the number of postersize signs.

signs that would result in the lowest cost to the council.

5 Practice #2: A student council is ordering signs for the winter dance. Signs can be made in letter size or poster size. No more than 30 of each size are wanted. No more than 50 signs are needed altogether. Lettersize signs cost $8.75 each, and postersize signs cost $14.50 each. Let 1 represent the number of lettersize signs. Let p represent the number of postersize signs. Write the objective function to determine the combination of the two sizes of signs that would result in the lowest cost to the council..4 Practice #3: A system of linear inequalities has vertices at (2, 6), (1, 4), (4, 6), and (0, 10). Which point represent the maximum value of the objective function W =0.5y+3x10? / ;ecffc ((,1)a1c()3)Io O,c(?F3 i)(o 4 (,t Practice #4 The following model represents an optimization problem. Determine the maximum solution and show your work. Restrictions: xew yew Constraints: x>0 y>0 x + 5 xiy10 Objective function: A=x+2 1 ) t2)15 f2c) ;13 >ctil) OiZg ;Q

6 ZVV. VVVV.V _VV.VV... Practice #5: A publisher makes romance and adventure novels. Romance novels sell for $10 and adventure novels for $8. The publishers noticed that each month they always sell between 500 and 800 romance novels and that the number of adventure novels sold is never more than double the number of romance novels sold. What are the maximum and minimum profits for a month? Y / FCt0 / V. 4c_ Z. ;. V I ( 0 j I j. ( o) /O(bO) (o ;5o) i). /ôvô

You may answer no more than 20 questions.

$() o3(,b) 3o i (o,2) o3)2o (O,L) O3C) 0., I I I,C). 6w,.\... 1..,..,..... r 2O :.$ $. \\ Co \\ r s 0 v c)e1 \JAR(A1Ve$ draw the feasible region, and create an$ worth 3 marks Multiple choice questions are worth 1 mark and openended questions

worth 3 marks Multiple choice questions are worth 1 mark and openended questions

7 You may answer no more than 20 questions. The total time for the test is 60 minutes openended question. () o3(,b) 3o i (o,2) o3)2o (O,L) O3C) 0., I I I,C). 6w,.\ ,..,..... r 2O :..: t, \.. \\ Co \\ r s 0 v c)e1 \JAR(A1Ve$ draw the feasible region, and create an objective function to maximize your score on the test. worth 3 marks Multiple choice questions are worth 1 mark and openended questions are Define the relevant variables, write an inequality for each constraint in the question, It takes 3 minutes to do a multiplechoice question and 6 minutes for an Practice #6: A test is made up of multiplechoice and openended questions.

Chapter 6 Outline Systems of Linear Inequalities

SOLVES AN INEQUALITY Chapter 6 Outline Systems of Linear Inequalities FORGETS TO FLIP THE SYMBOL Date Topic Homework Lesson 1: Exploring Linear Inequalities Homework Completion Complete In Progress Not