Section 9.5 – Linear Programming. (-3, 21) (0, -3) (-3, -3)

Slides:

Advertisements

Similar presentations

5.1 Modeling Data with Quadratic Functions. Quadratic Function: f(x) = ax 2 + bx + c a cannot = 0.

Advertisements

3.4 Linear Programming 10/31/2008. Optimization: finding the solution that is either a minimum or maximum.

Linear Programming?!?! Sec Linear Programming In management science, it is often required to maximize or minimize a linear function called an objective.

Completing the square Expressing a quadratic function in the form:

Solving Quadratic Equations by Graphing

Objectives: Set up a Linear Programming Problem Solve a Linear Programming Problem.

f has a saddle point at (1,1) 2.f has a local minimum at.

Systems of Linear Inequalities.  Two or more linear inequalities together form a system of linear inequalities.

Chapter 5 Linear Inequalities and Linear Programming Section R Review.

This is the graph of y = sin xo

3.1 Systems of Linear Equations Word Problems. Word Problems p.122 #37 37) To pay your monthly bills, you can either open a checking account or use an.

Objective: Cavalieri’s principle. Finding volume. Warm up 1. a.Sketch a horizontal cross-section of the rectangular prism. b.Find the its volume. Show.

Section 2.3 Properties of Functions. For an even function, for every point (x, y) on the graph, the point (-x, y) is also on the graph.

2.3 Analyzing Graphs of Functions. Graph of a Function set of ordered pairs.

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 7.6 Linear Programming.

LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You.

Section 1.3 – More on Functions. On the interval [-10, -5]: The maximum value is 9. The minimum value is – and –6 are zeroes of the function.

5.1 Modeling Data with Quadratic Functions Quadratic function: a function that can be written in the standard form of f(x) = ax 2 + bx + c where a does.

 Graph is a parabola.  Either has a minimum or maximum point.  That point is called a vertex.  Use transformations of previous section on x 2 and -x.

Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph of the function f to find the domain of f. 2.Find the.

Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will.

Warm-up Solve each system of equations:

5.2 Polynomials, Linear Factors, and Zeros P

Warm-up 4-1. x – y = 33x + y = 52y = 6 – x x + y = 5x – 2y = 43x – 2y = 6 Graphs:

Chapter 4: Systems of Equations and Inequalities Section 4.7: Solving Linear Systems of Inequalities.

5.2 Polynomial & Linear Factors Learning goals graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using.

Sec 2.5 Quadratic Functions Maxima and Minima Objectives: Express a quadratic in vertex form. Find coordinates of vertex by completing the square. Find.

Homework Assignment Pg: 429 (1-3 all,6-8 all, 18,21,28)

(0, 0) (36, 0) (30, 4) (0, 10) WARM UP: a. Graph the system of inequalities. b. What are the vertices of the solution? Write your answers as ordered pairs.

Big Idea: -Graph quadratic functions. -Demonstrate and explain the effect that changing a coefficient has on the graph. 5-2 Properties of Parabolas.

Linear Programming. What is linear programming? Use a system of constraints (inequalities) to find the vertices of the feasible region (overlapping shaded.

3.3 Linear Programming. Vocabulary Constraints: linear inequalities; boundary lines Objective Function: Equation in standard form used to determine the.

Section 3.5 Linear Programing In Two Variables. Optimization Example Soup Cans (Packaging) Maximize: Volume Minimize: Material Sales Profit Cost When.

Linear Programming Chapter 3 Lesson 4 Vocabulary Constraints- Conditions given to variables, often expressed as linear inequalities. Feasible Region-

Linear Approximations. In this section we’re going to take a look at an application not of derivatives but of the tangent line to a function. Of course,

2.6 Solving Systems of Linear Inequalities

Solving Nonlinear Systems

Section 5.1 Modeling Data with Quadratic Functions Objective: Students will be able to identify quadratic functions and graphs, and to model data with.

Straight Line Graphs (Linear Graphs)

ALGEBRA II HONORS/GIFTED SECTION 3-4 : LINEAR PROGRAMMING

PARENT GRAPH FOR LINEAR EQUATIONS

Chapter 5 Linear Inequalities and Linear Programming

3-3 Optimization with Linear Programming

Extreme Value Theorem Implicit Differentiation

Section 11.8 Linear Programming

Part (a) y = ex y = ln x /2 Area = (ex - ln x) dx

MATH 1311 Section 1.3.

What is the function of the graph? {applet}

Label Name Label Name Label Name Label Name Label Name Label Name

Section 2.3 – Analyzing Graphs of Functions

Section 4.4 – Analyzing Graphs of Functions

Graphical Solution of Linear Programming Problems

MATH 1311 Section 1.3.

X y y = x2 - 3x Solutions of y = x2 - 3x y x –1 5 –2 –3 6 y = x2-3x.

What is the function of the graph? {applet}

Analyzing Graphs of Functions

6-2 Polynomials & Linear Factors

Section Linear Programming

Linear and Nonlinear Systems of Equations

Linear and Nonlinear Systems of Equations

Linear Programming.

Section – Linear Programming

Intersection Method of Solution

Use Graphs of Functions

Presentation transcript:

Section 9.5 – Linear Programming

(-3, 21) (0, -3) (-3, -3)

a)Sketch a graph, labeling the points of intersection. b)Find the maximum value of z and state where it occurs. (0, 0) (36, 0) (30, 4) (0, 10) The maximum of 400 occurs at (30, 4)

a)Sketch a graph, labeling the points of intersection. b)Find the maximum value of z and state where it occurs. (0, 0) (0.5, 0) (0, 0.33) The maximum of 20 occurs at (0, 0.33)

a)Sketch a graph, labeling the points of intersection. b)Find the minimum value of z and state where it occurs. The minimum of 20 occurs at (20, 0) (0, 25) (10, 5) (20, 0)

a)Sketch a graph, labeling the points of intersection. b)Find the minimum value of z and state where it occurs. The minimum of 2 occurs at (2, 0) (2, 0) (10, 0) (0, 10) (0, 3)

a)Sketch a graph, labeling the points of intersection. b)Find the maximum value of z and state where it occurs. The maximum of 49 occurs at (5, 12) (6, 4) (3, 8) (5, 12) (3, 2)