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Plan for Today. Warm Up/Stamp Homework (green WS) Go Over Questions from Systems of Inequalities Quizzes from Friday/Monday are on-line Get back tomorrow 4.3 Notes 4.3 Worksheet Test Retakes are graded and on-line. x + y ≥ 6. x – 2 y &gt;10. 2. (10, 1). 1. (3, 3). 4. (15, 2). 3.

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Plan for Today
• Warm Up/Stamp Homework (green WS)
• Go Over Questions from Systems of Inequalities
• Quizzes from Friday/Monday are on-line
• Get back tomorrow
• 4.3 Notes
• 4.3 Worksheet
• Test Retakes are graded and on-line

x + y≥ 6

x – 2y>10

2.

(10, 1)

1.

(3, 3)

4.

(15, 2)

3.

(12, 0)

Warm Up

Determine if the given ordered pair is a solution of

no

no

yes

yes

3.4 Linear Programming
• Real Life Applications for Systems of Inequalities
• Inequalities represent the constraints of the problem (stipulations)
• Solution Region (Shaded region) is called the feasible region, represents the possibilities for the situation.
• Objective Function: How to maximize profit or minimize cost, maximize efficiency, etc.
Working the problem (identifying the minimum or maximum)
• Identify the variables in the problem
• Write a system of inequalities to describe the problem
• Graph the constraints (inequalities)
• All of these points in the feasible region are possibilities to the problem, but not necessarily the best choice
• Identify the Objective Function
• Identify the vertices of the feasible region (possible minimum and maximum solutions)
• Substitute each vertex into the objective function to find the minimum or maximum
Varying types of problems
• Given the constraints and the objective function
• Just a story/situation
Example 2

Yum’s Bakery bakes two breads, A and B. One batch of A uses 5 pounds of oats and 3 pounds of flour. One batch of B uses 2 pounds of oats and 3 pounds of flour. The company has 180 pounds of oats and 135 pounds of flour available.

Write the constraints for the problem and graph the feasible region. Set it up first…

Identify variables

• Write a system
• Graph

Yum’s Bakery wants to maximize its profits from bread sales. One batch of A yields a profit of \$40. One batch of B yields a profit of \$30. Use the profit information and the data from Example 1 to find how many batches of each bread the bakery should bake.

Write Objective Function

• Identify Vertices
• Substitute into objective function