6. Systems of Equations and Inequalities

Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

Linear Programming

Write Objective Function

Linear Programming Example

Linear Programming - Example 2

Writing Constraints and Objective Functions

Using Linear Programming to Solve Real World Problems with Constraints

In Exercises 1–4, find the value of the objective function at each corner of the graphed region. What is the maximum value of the objective function? What is the minimum value of the objective function? 1. Objective Function z=5x+6y <img src="https://lightcat-files.s3.amazonaws.com/problem_images/dc2efa2c0487378a-1675712281686.jpg" alt="" />

Write an Objective Function

Linear Programming (intro -- defining variables, constraints, objective function)

Find the value of the objective function z = 2x + 3y at each corner of the graphed region shown. What is the maximum value of the objective function? What is the minimum value of the objective function? <img src="https://lightcat-files.s3.amazonaws.com/problem_images/56a556cd8ac93ad1-1672429065205.jpg" alt="" />

In Exercises 1–4, find the value of the objective function at each corner of the graphed region. What is the maximum value of the objective function? What is the minimum value of the objective function? 1. Objective Function z=40x+50y <img src="https://lightcat-files.s3.amazonaws.com/problem_images/be2ea4a5a1245d47-1675713088491.jpg" alt="" />

In Exercises 5–14, an objective function and a system of linear inequalities representing constraints are given.
a. Graph the system of inequalities representing the constraints. 
b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/173928493afbadf4-1670240107772.jpg" alt="" />

In Exercises 5–14, an objective function and a system of linear inequalities representing constraints are given.
a. Graph the system of inequalities representing the constraints. 
b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.

In Exercises 5–14, an objective function and a system of linear inequalities representing constraints are given.
a. Graph the system of inequalities representing the constraints. 
b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/ba8597a53598665b-1670220931006.jpg" alt="" />

In Exercises 57–59, graph the region determined by the constraints. Then find the maximum value of the given objective function, subject to the constraints.  This  is a piecewise function. Refer to the textbook.

Linear Programming Word Problem - Example 1

Linear Programming 2: Graphical Solution - Minimization Problem

Represent constraints created by a system of inequalities

In Exercises 5–14, an objective function and a system of linear inequalities representing constraints are given.
a. Graph the system of inequalities representing the constraints. 
b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/d64180540da3ff05-1670224704450.jpg" alt="" />

In Exercises 5–14, an objective function and a system of linear inequalities representing constraints are given.
a. Graph the system of inequalities representing the constraints. 
b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/51c919016b3188dc-1670242675926.jpg" alt="" />

Represent constraints on solutions using systems of linear inequalities

Represent solutions and constraints to systems of linear inequalities by graphing

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