Algebra 2 3-4 Complete Lesson: Linear Programming

Posljednje ažuriranje over 4 years ago

Napomena autora:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

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Algebra 2 3-4 Complete Lesson: Linear Programming

Posljednje ažuriranje over 4 years ago

Napomena autora:

Solve It! You want to spend no more than $40 for at most 15 tomato plants. You want to maximize the pounds of tomatoes you'll get.

The variables are the number of roma (x) and cherry tomato plants (y) you buy. Graph both of the inequalities on the same plane.
Zoom and pan your graph to establish a suitable viewing window.

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.

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Use your graph to identify the combination of tomatoes that maximize the number of pounds that you can buy.

5 roma
2 cherry
10 cherry
10 roma

To maximize pounds

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Problem 1 Got It? Use the constraints from Problem 1 with the objective function P = x + 3y. What values of x and y maximize P?

(0, 2.5)

(0, 0)

(2, 0)

(3, 1)

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Problem 2 Got It?

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Graph the system of inequalities on the canvas below. Include relevant graph detail.
You may use the Desmos graphing calculator above to check your work. Shade each solution set using a different technique or color.

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Graph the system of inequalities on the canvas below. Include relevant graph detail.
You may use the Desmos graphing calculator above to check your work. Shade each solution set using a different technique or color.

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Graph the system of inequalities on the same coordinate plane.
Zoom and pan your graph to establish an appropriate viewing window.

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.

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Graph the system of inequalities on the same coordinate plane.
Zoom and pan your graph to establish an appropriate viewing window.

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.

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Graph the system of inequalities on the same coordinate plane.
Zoom and pan your graph to establish an appropriate viewing window.

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.

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Compare and Contrast: What are some similarities between solving a linear programming problem and solving a system of linear inequalities? What are some differences?

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Open-Ended: Graph a system of constraints whose graphs determine a trapezoid. Zoom and pan your graph to establish an appropraite viewing window.

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.

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Review Lesson 3-3: Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.

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Review Lesson 3-3: Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.

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Review Lesson 3-3: Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.

Objavili smo novi i poboljšani tip pitanja za grafički prikaz! Studenti više neće moći odgovoriti na ovo pitanje.

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Review Lesson 1-3: Evaluate each expression for a = 3 and b = -5. Match each expression with its value.

2a + b
-4 + 2ab
3(a - b)
b(2b - a)

24
-34
1
65

Review Lesson 2-4: Find the x- and y-intercepts of the graph of each linear function.

y-intercept: (0, -1)
x-intercept: (-3 , 0)
y-intercept: (0, 6)
x-intercept: (18, 0)
y-intercept: (0, 4)
x-intercept: (1, 0)

y = 2x+ 6
2x + 9y = 36
y = x - 1

Vocabulary Review: Label each polygon with its number of vertices.

quadrilateral
pentagon
octagon

Vocabulary Review: Identify the coordinates of each vertex in the diagram.

(6, 4)
(2, 1)
(0, 0)
(1, 2)
(3, 5)
(4, -1)
(5, 3)

Use Your Vocabulary: Complete the statement with the correct from the list. Enter only the word.
constraint
constrain
constrained
Weight is one ? on vehicles allowed on the bridge.

Use Your Vocabulary: Complete the statement with the correct from the list. Enter only the word.
constraint
constrain
constrained
An injury can cause ? motion.

Use Your Vocabulary: Complete the statement with the correct from the list. Enter only the word.
constraint
constrain
constrained
The rules of the game ? how you play.

100

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

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Algebra 2 3-4 Complete Lesson: Linear Programming

Algebra 2 3-4 Complete Lesson: Linear Programming

The variables are the number of roma (x) and cherry tomato plants (y) you buy. Graph both of the inequalities on the same plane.Zoom and pan your graph to establish a suitable viewing window.

Use your graph to identify the combination of tomatoes that maximize the number of pounds that you can buy.

Problem 1 Got It? Use the constraints from Problem 1 with the objective function P = x + 3y. What values of x and y maximize P?

Problem 2 Got It?

Graph the system of inequalities on the canvas below. Include relevant graph detail.You may use the Desmos graphing calculator above to check your work. Shade each solution set using a different technique or color.

Graph the system of inequalities on the canvas below. Include relevant graph detail.You may use the Desmos graphing calculator above to check your work. Shade each solution set using a different technique or color.

Graph the system of inequalities on the same coordinate plane.Zoom and pan your graph to establish an appropriate viewing window.

Graph the system of inequalities on the same coordinate plane.Zoom and pan your graph to establish an appropriate viewing window.

Graph the system of inequalities on the same coordinate plane.Zoom and pan your graph to establish an appropriate viewing window.

Compare and Contrast: What are some similarities between solving a linear programming problem and solving a system of linear inequalities? What are some differences?

Open-Ended: Graph a system of constraints whose graphs determine a trapezoid. Zoom and pan your graph to establish an appropraite viewing window.

Review Lesson 3-3: Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 3-3: Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 3-3: Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 1-3: Evaluate each expression for a = 3 and b = -5. Match each expression with its value.

Review Lesson 2-4: Find the x- and y-intercepts of the graph of each linear function.

Vocabulary Review: Label each polygon with its number of vertices.

Vocabulary Review: Identify the coordinates of each vertex in the diagram.

Use Your Vocabulary: Complete the statement with the correct from the list. Enter only the word.constraintconstrainconstrainedWeight is one __?__ on vehicles allowed on the bridge.

Use Your Vocabulary: Complete the statement with the correct from the list. Enter only the word.constraintconstrainconstrainedAn injury can cause __?__ motion.

Use Your Vocabulary: Complete the statement with the correct from the list. Enter only the word.constraintconstrainconstrainedThe rules of the game __?__ how you play.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

The variables are the number of roma (x) and cherry tomato plants (y) you buy. Graph both of the inequalities on the same plane.Zoom and pan your graph to establish a suitable viewing window.

Use your graph to identify the combination of tomatoes that maximize the number of pounds that you can buy.

Problem 1 Got It? Use the constraints from Problem 1 with the objective function P = x + 3y. What values of x and y maximize P?

Problem 4 Got It? Graphing: Graph the constraints from Problem 1 to form the feasible region. Zoom and pan your graph to establish a suitable viewing window.

Problem 2 Got It?

Graph the system of inequalities on the canvas below. Include relevant graph detail.You may use the Desmos graphing calculator above to check your work. Shade each solution set using a different technique or color.

Graph the system of inequalities on the canvas below. Include relevant graph detail.You may use the Desmos graphing calculator above to check your work. Shade each solution set using a different technique or color.

Graph the system of inequalities on the same coordinate plane.Zoom and pan your graph to establish an appropriate viewing window.

Graph the system of inequalities on the same coordinate plane.Zoom and pan your graph to establish an appropriate viewing window.

Graph the system of inequalities on the same coordinate plane.Zoom and pan your graph to establish an appropriate viewing window.

Compare and Contrast: What are some similarities between solving a linear programming problem and solving a system of linear inequalities? What are some differences?

Open-Ended: Graph a system of constraints whose graphs determine a trapezoid. Zoom and pan your graph to establish an appropraite viewing window.

Review Lesson 3-3: Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 3-3: Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 3-3: Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.

Review Lesson 1-3: Evaluate each expression for a = 3 and b = -5. Match each expression with its value.

Review Lesson 2-4: Find the x- and y-intercepts of the graph of each linear function.

Vocabulary Review: Label each polygon with its number of vertices.

Vocabulary Review: Identify the coordinates of each vertex in the diagram.

Use Your Vocabulary: Complete the statement with the correct from the list. Enter only the word.constraintconstrainconstrainedWeight is one __?__ on vehicles allowed on the bridge.

Use Your Vocabulary: Complete the statement with the correct from the list. Enter only the word.constraintconstrainconstrainedAn injury can cause __?__ motion.

Use Your Vocabulary: Complete the statement with the correct from the list. Enter only the word.constraintconstrainconstrainedThe rules of the game __?__ how you play.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Problem 4 Got It? Graphing: Graph the constraints from Problem 1 to form the feasible region. Zoom and pan your graph to establish a suitable viewing window.

The variables are the number of roma (x) and cherry tomato plants (y) you buy. Graph both of the inequalities on the same plane.
Zoom and pan your graph to establish a suitable viewing window.

Graph the system of inequalities on the canvas below. Include relevant graph detail.
You may use the Desmos graphing calculator above to check your work. Shade each solution set using a different technique or color.

Graph the system of inequalities on the canvas below. Include relevant graph detail.
You may use the Desmos graphing calculator above to check your work. Shade each solution set using a different technique or color.

Graph the system of inequalities on the same coordinate plane.
Zoom and pan your graph to establish an appropriate viewing window.

Graph the system of inequalities on the same coordinate plane.
Zoom and pan your graph to establish an appropriate viewing window.

Graph the system of inequalities on the same coordinate plane.
Zoom and pan your graph to establish an appropriate viewing window.

Use Your Vocabulary: Complete the statement with the correct from the list. Enter only the word.
constraint
constrain
constrained
Weight is one ? on vehicles allowed on the bridge.

Use Your Vocabulary: Complete the statement with the correct from the list. Enter only the word.
constraint
constrain
constrained
An injury can cause ? motion.

Use Your Vocabulary: Complete the statement with the correct from the list. Enter only the word.
constraint
constrain
constrained
The rules of the game ? how you play.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.

The variables are the number of roma (x) and cherry tomato plants (y) you buy. Graph both of the inequalities on the same plane.
Zoom and pan your graph to establish a suitable viewing window.

Graph the system of inequalities on the canvas below. Include relevant graph detail.
You may use the Desmos graphing calculator above to check your work. Shade each solution set using a different technique or color.

Graph the system of inequalities on the canvas below. Include relevant graph detail.
You may use the Desmos graphing calculator above to check your work. Shade each solution set using a different technique or color.

Graph the system of inequalities on the same coordinate plane.
Zoom and pan your graph to establish an appropriate viewing window.

Graph the system of inequalities on the same coordinate plane.
Zoom and pan your graph to establish an appropriate viewing window.

Graph the system of inequalities on the same coordinate plane.
Zoom and pan your graph to establish an appropriate viewing window.

Use Your Vocabulary: Complete the statement with the correct from the list. Enter only the word.
constraint
constrain
constrained
Weight is one ? on vehicles allowed on the bridge.

Use Your Vocabulary: Complete the statement with the correct from the list. Enter only the word.
constraint
constrain
constrained
An injury can cause ? motion.

Use Your Vocabulary: Complete the statement with the correct from the list. Enter only the word.
constraint
constrain
constrained
The rules of the game ? how you play.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.