algebra 2 2014-2015

Algebra 2 2014-2015

Second Six Weeks October 6 – November 14, 2014

Monday Tuesday Wednesday Thursday Friday

October 6 B Day 7 A Day 8 B Day 9 A Day 10 B Day 3.2 Substitution and Elimination -from contexts, write equations, determine best method to use, define variables and solve. -2 variable

3.3 Substitution and Elimination -continue solving -3 variable (NEW)

3.4 Solving systems with matrices -Setting up matrices from systems of equations - solving systems with matrices

13 14 A Day 15 B Day 16 A Day 17 B Day

No School

Professional

Development

Day

Flex Day 3.5 Linear Programming -Writing Equations and inequalities -Graphing Restraints -Find critical points and calculate max and mins

20 A Day 21 B Day 22 A Day 23 B Day 24 A Day

Unit 3 Elaboration/Flex Day

4.1 Representations of Quadratic Functions -analyze & predict using quadratic data -make scatterplot -graph and look at tables -quadratic regression

27 B Day 28 A Day 29 B Day 30 A Day 31 B Day 4.1 Representations of Quadratic Functions -analyze & predict using quadratic data -make scatterplot -graph and look at tables -quadratic regression

4.2 Transforming Quadratics -up/down, left/right, horz/vert stretch/compression

-domain/range in inequality, interval & set notaion Begin 4.3

4.3 Three forms of a Quadratic -discuss factored, vertex, and standard form, their characteristics and uses

-complete the square to move from standard to vertex

Nov 3 A Day 4 B Day 5 A Day 6 B Day 7 A Day 4.4 Parabola Conics day 1 -graph and identify key attributes (vertex, focus, directrix, axis of symmetry, direction of opening) -write equation given attributes

4.5 Parabola Conics day 2

Unit 4

Elaboration/Flex

10 B Day 11 A Day 12 B Day 13 A Day 14 B Day Unit 4

Elaboration/Flex

Reteach 4A 4.6 Solve by graphing -use calculator -solve linear & quadratic intersection(s) (NEW) -Look at zeros/roots/x-intercepts and solutions on a graph by hand and on calculator

UNIT 3 TEST

UNIT 4A TEST

PSAT

Algebra 2 3.1 Explore: Systems by Graphing

Name _____________________ Period _____

Solving Systems of Equations by Graphing EXPLORE Your Company, Calls R Us, has asked you to submit a report on cellular phone service plans. Using past phone bills from a previous plan, you notice company employees’ use approximately 600 minutes of airtime per month. Use the information on the internet to compare 600 minute phone plans in your area. Your boss has provided you with the following printout from the web to help you with your research.

Comparison Calculator

Lady Blah Blah Yakity Yak Cellular Monthly Access Fee Additional Minutes

Fill in the table with the individual cost under each plan for the number of additional minutes given.

Lady Blah Blah Wireless Yakity Yak Cellular

Total Minutes Additional

minutes Process Cost Process Cost

600 0

650 50

700 100

750 150

600+x x

Lady Blah Blah Wireless Yakity Yak Cellular

User Rating (N/A)

Monthly Fee $ 75.00 $ 89.99

Minutes Included Anytime: 600 minutes Anytime: 600 minutes

Contract Term 12 months 12 months

Activation Fee $25.00 $25.00

Cancellation Fee $175.00 $120.00

Additional Minute Rate ($/min) $0.35 $0.25

First Free Minute No No

Incremental Billing 1 minute 1 minute

Coverage Type National National

Digital/Analog Digital Digital

Algebra 2 3.1 Explore: Systems by Graphing

1. What is the range of (a)Lady Blah Blah? __________________ (b)Yakity Yak? _________________

2. Using the information in the table above, write equations to model each long distance rate plan.

LBB Plan: ________________ YY Plan: __________________ 3. Use your graphing calculator

and create the graphs for this situation. Sketch your graphs and label.

4. From your graph, determine the Y/Cost-intercepts (b-value) for each plan’s equation.

LBB: ________________ YY:_____________________

What do these Y-intercepts/Cost-axis intercepts represent in this problem? (Hint: the answer is not “the place where the lines cross the y-axis.”) Explain why the cost-axis intercepts are different for the two plans.

5. What is the Slope (m - value) for each of your lines of best fit?

LBB: __________________ YY: __________________ What do these values represent? __________________________________

6. Which Plan would you recommend to a customer who uses a total of 635 minutes a month? Why?



9. Do the lines of the graphs cross? ____________ Point of intersection________________ 10. What is the meaning of this point of intersection?

What would it mean if they NEVER crossed? How many solutions would that produce? What would it mean if they ALWAYS crossed? How many solutions would that produce?

Algebra 2 3.1 Explain: Systems by Graphing

When there are two linear equations with two unknown variables, you can use a system of equations to find the variables. Possible Outcomes:

If, when you graph the two lines they intersect in ONE POINT, this point is the SOLUTION to the system of equations.

If, when you graph the two lines they do NOT intersect, then the lines are PARALLEL and there are NO solutions.

If, when you graph the two lines they are the SAME line, then the lines are the SAME and there are INFINTELY MANY solutions.

Graph the following lines to find where they intersect each other.

1.

y x 2

y x 2

Answer: ___________ 2.

y 1

2x 3

y 2x 1

Answer: ___________

Finding Intersection using Graphing Calculator: 1. Y= Enter equations for 2 functions in Y1 and Y2

Using Table… 2. 2nd-GRAPH Find where Y1 and Y2 are the same Using Graph.. 2. GRAPH Zoom or set window to see intersection 3. 2nd-TRACE-5-ENTER-ENTER-ENTER Intersection listed at bottom of window

Use your calculator to find the solution to the following systems of equations.

3.

y x 7

y x 9

4.

y 3x 4

y 0.5x 6

Answer: ___________ Answer: ___________

Algebra 2 3.1 Explain: Systems by Graphing

Transform the following equations into y = mx + b form (slope-intercept form) SHOW YOUR WORK,

and then use your calculator to find the solution to each system.

5.

x y 27

3x y 41

Answer: ___________ 6.

5x 4y 26

4x 2y 53.3

Answer: ___________

Use a table to solve the system of equations.

7. 2 4

3 44

y x

y x

Answer: ___________ 8.

4 1

4 8

y x

y x

Answer: ___________

9. 11

11

x y

x y

Answer: ___________ 10. 6 2 2

3 7 17

x y

x y

Answer: ___________

For each table write an equation in slope-intercept form. Then solve the system. (By graphing or using your calculator) 11. Solution:

y = _______________ y = _______________ 12.

Solution:

y = _______________ y = _______________

x y

0 -30

2 -26

4 -22

x y

-2 5

0 3

2 1

x y

0 5

2 7

4 9

x y

-2 0

0 -2

2 -4

Algebra 2 3.1 Evaluate: Systems by Graphing

The school band decides to sell chocolate bars to raise money for an upcoming trip. The cost and the revenue of selling the candy bars are represented on the graph below.

Candy Bar Sales

1. At what point do the two graphs intersect? 2. What would be the revenue from selling 50 candy bars? 3. What would the revenue be from selling 125 candy bars? 4. How many candy bars must the band sell for the revenue to be $200? How much of this revenue

would be profit? Graph the following lines to find where they intersect each other. Show all your work needed.

5.

y x 2

y x 2

5. 6.

Answer: ___________

6.

12

621

yx

yx

Answer: ___________

200 150 100 50 0

Dol

lars

0 50 100 150 200 250 300

Number of Bars Sold

Cost

Revenue

Algebra 2 3.1 Evaluate: Systems by Graphing The new movie theater opened in Regal’s neighborhood. The theater offers a yearly membership for which customers pay a fee of $50, after which they pay only $1 per movie. Nonmembers pay $4.50 per movie. Regal is trying to figure out whether to buy a membership. She writes these cost equations.

C M = 50 + n C N = 4.5n

Where n is the number of movies seen in one year, C M is the yearly cost in dollars for a member, and C N is

the yearly cost in dollars for a nonmember. 7. If Regal sees ten movies this year, what would be her cost under each plan? 8. Complete the table below and then draw a graph from the data. Use a different color for each line.

9. How many movies must Regal see this year to make the yearly membership a better deal? 10. What does the y-intercept in each equation tell you about this situation? 11. What does the coefficient of n in each equation tell you about the situation?

# of Movies

Member Cost

Nonmember Cost

0

2

4

6

8

10

12

14

16

18

20

Algebra 2 3.2 Explain: Substitution & Elimination

Solving Systems by Substitution Explain (Notes) – Powerpoint Example 1

2

12

y x

x y

Substitute

2 12x x Simplify

3 12x Solve

4x Plug in to the first equation

2(4)

8

y

y

Answer

( , ) (4,8)x y Example 2

3 20

12

b a

a b

( , ) (__, __)a b

Example 3

22 4

9 2

T p

p T

Answer ( , ) (__, __)p T

Example 4

3 1

2 9

x y

x y

Answer ( , ) (__, __)x y

Algebra 2 3.2 Explain: Substitution & Elimination

Elaborate (Word Problems) Use the substitution method to solve these word problems. 1. An art class is planning a trip to a museum. There are 22 people on the trip. There

are 4 drivers and 2 types of vehicles, vans and cars. The vans seat 6 people and cars seat 4 people, including drivers. How many vans and cars does the class need for the trip?

Define variables: v = _________________ c = __________________ Set up a system of equations and solve: Solution: v = ____________ c = ______________

2. Find two numbers whose sum is 121 and whose difference is 55. Define variables: x = _________________ y = __________________ Set up a system of equations and solve: Solution: x = ____________ y = ______________

3. You have 14 coins in nickels and dimes. If your coins total $1.00, how many of each

do you have? Define variables: x = _________________ y = __________________ Set up a system of equations and solve: Solution: x = ____________ y = ______________

Algebra 2 3.3 Elaborate: Substitution & Elimination

Rally Robin- Solving Systems by Substitution

In one week, a music store sold 9 guitars for a total of $3911. Electric guitars sell for $479 each and acoustic guitars sell for $399 each. How many of each guitar was sold?

a. Define the variables

b. Set up a system of equations

c. Using substitution, solve for one of the variables.

d. Using the answer in part ‘c’, solve for the other variable.

e. Write the answer as an ordered pair.

f. Write the answer in a complete sentence.

Partner 1

Name__________________________

Partner 2

Name_________________________

Algebra 2 3.3 Elaborate: Substitution & Elimination

One evening, 76 people gathered to play singles and doubles tennis. There were 26 games in progress at one time. A doubles game requires 4 players and a singles game requires 2 players. How many of each game were played? a. Define the variables

b. Set up a system of equations

c. Using substitution, solve for one of the variables.

d. Using the answer in part ‘c’, solve for the other variable.

e. Write the answer as an ordered pair.

f. Write the answer in a complete sentence.

Partner 2

Name__________________________

Partner 1

Name_________________________

Algebra 2 3.2 Evaluate: Substitution & Elimination Name __________________ Period ______

Solving Systems by Substitution and Elimination

Solve the system of equations for each problem using substitution method.

1. 3 11

2 8

x y

x y

2.

6 2 5

3 7

x y

x y

Solution: ____________________ Solution: _______________________

3. 3 7 13

3 7

x y

x y

4.

2 5 10

3 36

x y

x y


Solve the system of equations for each problem using ELIMINATION method.

5. 2 6 17

2 10 9

x y

x y

6.

10 2 16

5 3 12

x y

x y


Algebra 2 3.2 Evaluate: Substitution & Elimination Name __________________ Period ______

7. 3 4 18

6 8 18

x y

x y

8.

7 2 11

2 3 29

x y

x y

Solution: ____________________ Solution: _______________________ Solve the system of equations for each problem. Show all work. 9. Two angles are supplementary; that is, the sum of their measures is 180 degrees. The measure of one angle is 30 degrees more than twice the other. What is the measure of each angle? 10. The width of a patio is 5 feet less than twice its length. The difference between the length and width is 1 foot. Find the dimensions of the patio. 11. You have 12 coins in quarters and dimes. If your coins total $1.95, how many of each do you have?

Algebra 2 3.2 Explain: Elimination

Page 1 of 3

Solving Systems by Elimination (Stations)

Adding or subtracting equations: When both linear equations of a system are in the form ___________________, you can solve the system using ________________. You can add or subtract the equations to eliminate a variable.

5x – 6y = -32 3x + 6y = 48 ============== Solution:

3x – y = 21 2x + y = 4 ============== Solution:

Suppose your class receives $1,084 for selling 205 packages of greeting cards and gift wrap. Let w = the number of packages of gift wrap and c = the number of packages of greeting cards sold. Use a system to find the number of each type of package sold. Gift wrap cost $4 and cards cost $10.

5a + 6b = 54 3a – 3b = 17 ============== Solution:


Page 2 of 3

Station Rotation

2r – 3n = 13 8r + 3n = 7

2p – 5q = 6 4p + 3q = -1

3u + 4w = 9 -3u – 2w = -3

4x – 2y = 3 5x – 3y = 2

h = 2s – 1 2s – h = 1

a + s = 292 3a + s = 470


Page 3 of 3

1. A grocer bought 4 crates of lettuce and 3 crates of cabbage. Later he bought 2 crates of lettuce and 5 crates of cabbage. His first bill was $34.20 and the second bill was $31.80. Find the cost of each crate of lettuce and each crate of cabbage.

2. The sum of two numbers is 32. One of the numbers is 4 less than 5 times the other. Find the two numbers.

3. A man invests $17,000 in two accounts. One account earns 5% interest per year and the other 6.5%. If his yearly yield in interest is $970, how much does he invest at each rate?

4. You have 12 coins in quarters and dimes. If your coins total $1.95, how many of each do you have?

5. A will states that John is to get 3 times as much money as Mary. The total amount they will receive is $11,000. How much will each get?

Algebra 2 3.3 Evaluate: Substitution & Elimination

Name:_____________________ Solve the system of equations for each problem. Show all work on your own paper. 1. A grocer bought 4 crates of lettuce and 3 crates of cabbage. Later he bought 2 crates of lettuce and

5 crates of cabbage. His first bill was $34.20 and the second bill was $31.80. Find the cost of each crate of lettuce and each crate of cabbage.

2. The sum of two numbers is 32. One of the numbers is 4 less than 5 times the other. Find the two

numbers. 3. A man invests $17,000 in two accounts. One account earns 5% interest per year and the other

6.5%. If his yearly yield in interest is $970, how much does he invest at each rate? 4. You have 12 coins in quarters and dimes. If your coins total $1.95, how many of each do you have? 5. An art class is planning a trip to a museum. There are 22 people on the trip. There are 4 drivers

and 2 types of vehicles, vans and cars. The vans seat 6 people and the cars seat 4 people, including drivers. How many vans and cars does the class need for the trip?

6. A will states that John is to get 3 times as much money as Mary. The total amount they will receive

is $11,000. How much will each get?

Algebra 2 3.3 Evaluate: Substitution & Elimination

Name:_____________________ 7. Two angles are supplementary; that is, the sum of their measures is 180 degrees. The measure of

one angle is 45 degrees more than twice the other. What is the measure of each angle? 8.. At Garvin’s Department Store, Martha and Laura found shirts on sale at one price, shoes on sale at

another price and pairs of jeans for a third price. Martha bought 3 skirts, 2 pairs of shoes, and 2 pairs of jeans for $185. Laura bought 1 shirts, 2 jeans, and 2 pairs of shoes for $120. Find the sale price of each item.

9. The biggest angle of triangle is 4 more than twice the smallest angle. The smallest angle is 24 less than the middle angle. Find the measure of all three angles.

10. You have a combination of nickels, dimes, and quarters that total $ 2.75. There are 21 coins. The

number of dimes is twice the number of nickels. How many nickels, dimes, and quarters do you have?

Algebra 2 3.4 Explain: Solving Systems using Matrices 1. What are the dimensions of the following matrices? (“row” by “column”)

A =

530

142 B =

0

3

2

C =

71

24 D =

e2

1

921

052

____________ _____________ ______________ ______________ 2. Review the process for solving for x with these equations.

a. 43

2x b. 4x = 12 c.

8

7

5

3x

To solve these equations, we multiplied both sides of the equation by the ________________, also known as the multiplicative _______________. So far we have learned three methods we can use to solve a system of equations. They are: 1) _________________, 2) __________________, and 3) __________________. Now we will learn another method for solving systems of linear equations. 3. Write the following system of equations in matrix form. 2x + 3y = 7 4x + 7y = 15

Just as we solved the equation 43

2x by using the inverse of

3

2, we can solve the matrix equation by using

its inverse. Solve the matrix equation by multiplying both sides of the equation by the inverse of [A], or [A]-1.

15

7

74

32

y

x

1

74

32

y

x

74

321

74

32

15

7

Algebra 2 3.4 Explain: Solving Systems using Matrices

y

x1

74

32

15

7

In your calculator, you can now solve the equation by entering

1

74

32

as [A]-1. To do this, follow these steps:

a. Push ALPHA then ZOOM

b. Set dimensions of matrix and press enter

c. Enter elements into matrix

d. Arrow to the right and push the X-1

button

Now enter matrix [B] into the calculator:

a. Push ALPHA then ZOOM b. Set dimensions of matrix and press enter

c. Enter elements into matrix

d. Push ENTER

What is on your screen now? ________ This answer is in matrix form. The value for x is ____ and the value for y is ____. Your Turn! Apply this method to solve the following 3-variable linear system.

Given

30324

1743

12

zyx

zyx

yx

write in matrix form:

z

y

x

Solve using [A]-1[B]. The answer is

. Thus, the final answer is x = ___, y = ___, and z = ___.

Algebra 2 3.4 Elaborate: Solving Systems using Matrices Name _____________________ Date ______________ Per ____ Application Problems There are many real-life situations that can be modeled by a 3-variable system of equations. Given the following scenarios: a. Write a system of equations to describe the situation. b. Put the system into matrix form and solve. c. Use the solution to answer the questions in context. 1. On a recent trip to the movies, three students, Noah Lott, Carey Ahn, and Rita Book each spent some

money at the concession counter. Noah bought 2 candy bars, 2 small drinks and 2 bags of popcorn for a total of $5.36. Carey spent $4.17 on 1 candy bar, 2 small drinks, and a bag of popcorn. Meanwhile, Rita bought 3 bags of popcorn and 2 small drinks and no candy bars. She spent $5.86. If no tax was included in these totals, what was the purchase price of each item?

2. Linda, Kelly, and Amy all went to the matinee. Linda took her two children and her mother, who is a senior

citizen. She paid $12. Kelly took her two children and her mother, who is not a senior citizen. She paid $13. Amy took her son, her husband, and her mother and father, both of whom are senior citizens. She paid $16.50. What are the matinee prices for adults, children, and senior citizens?

Algebra 2 3.4 Evaluate: Solving Systems using Matrices

Matrix Applications Worksheet Name ______________________ Date _____________ Per ______ Write a linear system with the information given in each problem, set up a matrix, then solve. Show all work (variables defined, linear system, matrix) and write your answer in a sentence. 1. Admission for a talent show was $1.25 for adults and $.50 for children, and the receipts totaled $406.75. If 512 people attended, how many adults and how many children were there? 2. A collection of dimes and quarters is worth $19. There are 91 coins in all. How many of each are there? 3. Dillon bought 3 hot dogs and 2 candy bars for $4.50, and Andy bought 1 hot dog and 4 candy bars for $4.00. How much did each item cost? 4. At a furniture store, one sofa and one love seat cost $1100; one sofa and three chairs cost $1600; and one sofa, one love seat, and one chair cost $1400. What is the price of one sofa?


5. The feed mill pays a farmer $6930 for the 1st delivery, $5475 for the 2nd delivery, and $8879.50 for the 3rd delivery. The table shows the number of bushels included in each delivery. Find the price per bushel that the farmer received for each crop.

Delivery Corn Wheat Soybeans

1st 900 540 360

2nd 1125 150 225

3rd 860 645 645

6. The movie theater charges $4 for children, $6 for adults, and $5 for senior citizens. A group of 14 people from a family went to see a movie. There were an equal number of children and

senior citizens. The total cost was $66. Let x represent children, y represent adults, and z represent senior citizens. How many people in the group were in each age category?


7. The Nut Company sells made to order trail mixes. Zack’s favorite nut mix contains peanuts, raisins, and carob-coated pretzels. Peanuts sell for $3.20 per pound, raisins sell for $2.40 a pound, and carob- coated pretzels are $4.00 a pound. Sam bought a 5 pound mixture for $16.80 that contained twice as many pounds of carob coated pretzels as raisins. How many pounds of peanuts, raisins, and carob- coated pretzels did Sam buy? 9. ACT/SAT. Each year at Lake High School the students vote to choose that year’s prom theme. The theme “A Night Under the Stars” received 225 votes, and the theme “The Time of My Life” received 480 votes. If 40% of girls voted for “A Night Under the Stars” , and 75% of boys voted for “The Time of My Life”, and all of the students voted, how many girls and boys are there at Lake High School?

Algebra 2 3.5 Explore/Explain/Evaluate: Linear Programming

Page 1 of 7

Name __________________ Period ______

Linear Programming – Day 1

Explore (Activity) – Larry’s Landscaping

Larry’s Landscaping company has crews who mow lawns and prune shrubbery. The company schedules 1 hour for mowing jobs and 2 hours for pruning jobs. Each crew is scheduled for no more than 2 pruning jobs per day. Each crew’s schedule is set up for a maximum of 9 hours per day. On the average, the charge

for mowing a lawn is $40 and the charge for pruning shrubbery is $120. Find a combination of mowing lawns and pruning shrubs that will maximize the income the company receives per day for one of its crews. Step 1

Organize the information into this table: Mowing Lawns

x Pruning Shrubs

y Constraining

value

Time (hours) Step 2 Use your table to help you write inequalities that reflect the constraints given, and be sure to include any commonsense constraints. Let ‘x’ represent the number of mowing lawns, and let ‘y’ represent the number of pruning shrubs. (Hint: you should have 4 inequalities. Consider the least number of lawns they can mow and the least numbers of shrubs they can prune)


Page 2 of 7

Step 3 Graph the feasible region to show the combinations of lawns mowed and shrubs pruned the landscaping company could schedule, and label the coordinates of the vertices.

Step 4 It will make sense to produce only whole numbers of lawns mowed and shrubs pruned. List the coordinates of all integer points within the feasible regions. Remember that the feasible region may include points on the boundary lines. DON’T WORRY ABOUT THE PROFIT COLUMN YET!

Point Profit Point Profit Point Profit Point Profit

(0, 0) (2, 1) (0, 2)

(1, 0) (3, 1) (1, 2)

(2, 0) (8, 0) (2, 2)

(3, 0) (9, 0)

(0, 1) (6, 1)

(1, 1) (7, 1) (5, 2)


Page 3 of 7

Step 5 Write the equation that will determine profit based on the number of lawns mowed and shrubs pruned scheduled. Calculate the profit that the company would earn at each of the feasible points you found in Step 3. You may want to divide the values up among your group members. Before you go on, check your equation with the teacher.

Profit = ______ x + ______ y

Use this space to calculate the values if necessary.

(x, y) = 40x + 120y

(___, ___) = 40(___) + 120(___) = _______ + ______ = __________ (___, ___) = 40(___) + 120(___) = _______ + ______ = __________ (___, ___) = 40(___) + 120(___) = _______ + ______ = __________ (___, ___) = 40(___) + 120(___) = _______ + ______ = __________ (___, ___) = 40(___) + 120(___) = _______ + ______ = __________ (___, ___) = 40(___) + 120(___) = _______ + ______ = __________ (___, ___) = 40(___) + 120(___) = _______ + ______ = __________ (___, ___) = 40(___) + 120(___) = _______ + ______ = __________ (___, ___) = 40(___) + 120(___) = _______ + ______ = __________ (___, ___) = 40(___) + 120(___) = _______ + ______ = __________ (___, ___) = 40(___) + 120(___) = _______ + ______ = __________ (___, ___) = 40(___) + 120(___) = _______ + ______ = __________ Go back and fill in the profit column now!

Step 6 What number of each kind of appointment should Larry’s Landscaping schedule to maximize profit?

Lawns Mowed = __________

Pruned Shrubs = __________

Maximum profit = __________

Plot this point on your feasible graph. What do you notice about this point? _________________________________________________________________________________________


Page 4 of 7

Explain (Notes) Linear programming is a ‘real-world’ example of using systems. Usually we use linear programming when wanting to maximize or minimize something. First we need to remember how to graph a system of inequalities. Graph the following: Example 1

1

6

2025

4045

x

y

xy

xy

Example 2

0

4

2

y

x

xy

yx


Page 5 of 7

The ‘shaded’ area is called a feasible region. You will need to be able to find all the ‘corner’ points which are called vertices. Example 3 Find the vertices on the following pictures. Vertices: Every linear programming problem has an objective function. This is a function that represents what we are trying to maximize. For example, we might want to maximize or profit, or a score on an exam. Once we have an objective function and vertices, we can find the maximum and minimum values of that graph. Is the point (6, 4) included in the feasible region? Example 5: Graph the following constraint inequalities and then find the maximum and minimum vales for the given objective function.

1

6

2025

4045

x

y

xy

xy

P = 8x + 2y Max_________ Min_________

Feasible

region


Page 6 of 7

Evaluate (Assignment) – Due on ___________________ 1. A linear programming problem gives (0, 0), (0, 90), (50, 80), (70, 20), and (70, 0) as consecutive vertices of the feasible region. Find the maximum and minimum

values of the objective function. P = 3x + 4y in the feasible region. 2. A linear programming problem give (10, 0), (10, 40), (30, 50) and (40, 20) as the

consecutive vertices of the feasible region. Find the maximum and minimum value of the objective function P = 13x - 5y in the feasible region.


Page 7 of 7

#3-4: Graph the following constraint inequalities and then find the maximum and minimum vales for the given objective function.

3.

0

4

2

y

x

xy

yx

P = x + 3y Max_______ Min_______

4.

3

1

3065

1243

x

x

yx

yx

P = x - 2y Max_______ Min_______

Station I

State the BEST way to solve each system (substitution, elimination, matrices, or graphing) and then

solve using any method you like.

Write your answer as an ordered pair.

1.

x5y

7y2x4 2.

12y8x

68y12x

3.

6yx

20y2x 4.

13yx5

12y3x2

5. 3x y 4

2y 6x 8

6.

x 2y z 0

2x 5y 4z 1

x y 9z 5

Station II

Write a system of equations for each and solve.

1. To raise money for new uniforms, the school booster club sells silk-screened T-shirts. Short sleeve T-

shirts cost the school $8 each and are sold for $11 each. Long sleeve T-shirts cost the school $10 each

and are sold for $16 each. The club spends a total of $3900 on T-shirts and sells all of them for $5925.

How many of the short sleeve T-shirts are sold?

A) 75 B) 150 C) 175 D) 250

2. Three hamburgers and two orders of fries cost $6.10. Four hamburgers and three orders of fries

cost $8.40. At these rates, what is the cost of one hamburger and the cost of one order of fries?

3. Karen has $4.60 in dimes and quarters. She has 10 more quarters than dimes. How many dimes does

she have?

4. The beach resort is offering two weekend specials. One includes a 2–night stay with 3 meals and

costs $195. The other includes a 3-night stay with 5 meals and costs $300. What is the cost of

staying one night at the beach resort?

5. The math club wants to order shirts with their school logo. One company charges $9.65 per shirt

plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. For what number of

shirts would the cost be the same?

6. At Hamburger Haven, Tom buys 3 hamburgers and 2 fries for $14.

Sue buys 1 hamburger and 4 fries for $8. Write a system and solve

graphically to find the cost of each hamburger and each bag of fries.

System:

Hamburger: _________

Fries: __________

Station III

1. The sum of three numbers is -2. The sum of three times the first number, twice the second number,

and the third number is 9. The difference between the second number and half the third number is 10.

Find the numbers.

2. Mary, Jaime, and Renee went on a shopping spree to get ready for college. Mary brought three shirts,

four pair of pants, and two pair of shoes costing a total of $149.79. Jaime came away with five shirts,

three pair of pants, and three pair of shoes totaling $183.19. Renee bought six shirts, five pair of pants,

and a pair of shoes. Her total bill came to $181.14. Assuming that like items cost the same amount, find

the cost of each item.

3. On a recent trip to a football game, Ashley, Wendy, and Christina each purchased snacks. Ashley

bought 3 candy bars, 2 drinks, and 2 bags of peanuts for $6.65. Wendy spent $7.05 on a candy bar, 2

drinks, and 4 bags of peanuts. Christina spent $9.10 on 5 drinks and 3 bags of peanuts. What was the

price of a bag of peanuts?

Station IV

Solve the following systems graphically and write the solution in the blank.

1.

822

3

xy

xy 2.

103

3

yx

yx

_________ _________

3.

4

72

xy

yx

_________

4. Write the equations of the inequalities shown below:

5. The SPCA has 3 times as many dogs as cats. They have a total of 60 animals. Which of the following

represents a feasible region for the number of dogs and cats at the SPCA if they want to keep their

number of animals below the numbers they have now?

Station V 1. True or False: Any point in the feasibility region may be a maximum or a minimum point? 2. True or False: Given P = 2x + 7y. If the feasibility region has vertices (0, 3), (2, 4)

and (5, 2), then the maximum value is 24.

Station VI 1. Identify which matrix is not allowed:

11 2 1 0

2 5 4 1

1 1 9 5

x

y

z

10

2 4 1

1 1 5

x y z x

y y

z z

algebra 2 2014-2015

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