get out your vertices worksheet! you will be able to find the maximum and minimum values of a...
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Get out your Vertices Worksheet!
You will be able to find the maximum and minimum values of a function over a region.
You will be able to solve real-world optimization problems using linear programming.
Today’s Objectives:
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Warm UpGraph the following system of inequalities. Find the coordinates of the THREE vertices.
Solve the system of equations.2. by Substitution 3. by Elimination
Jackie has a total of 50 nickels and pennies. She has 13 more pennies than nickels. How many of each does she have?
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3.3 Linear Programming
New Vocabulary:
1. Linear Programming-
2. Feasible Region-
3. Bounded-
4. Unbounded-
5. Optimize-
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3.3 Linear Programming
Linear Programming:
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3.3 Linear Programming
Feasible Region:
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Bounded vs. UnboundedThe feasible region is enclosed, or bounded, by the constraints. The maximum and minimum always occur at a vertex.
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Bounded vs. UnboundedThe feasible region is open, or unbounded, and can go on forever.
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Bounded ExampleGraph the following system of inequalities. Name the coordinates and find the vertices of the feasible region. Find the maximum and minimum values of this region.
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Unbounded ExampleGraph the following system of inequalities. Name the coordinates and find the vertices of the feasible region. Find the maximum and minimum values of this region.
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ExamplesGraph the following system of inequalities. Name the coordinates and find the vertices of the feasible region. Find the maximum and minimum values of this region.
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𝒅
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You Try One!Graph the following system of inequalities. Name the coordinates and find the vertices of the feasible region. Find the maximum and minimum values of this region.
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Linear Programming—Optimization
Optimize:
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7 Steps of Optimization
Step 1: Define the variable
Step 2: Write a system of inequalities
Step 3: Graph the system of inequalities
Step 4: Find the coordinates of the vertices of the feasible region.
Step 5: Write a linear function to be maximized or minimized.
Step 6: Substitute the coordinates of the vertices into the function.
Step 7: Select the greatest or least result. Answer the problem.
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Linear Programming WorksheetEach week, Mackenzie can make 10 to 25 necklaces and 15 to 40 pairs of earrings. If she earns profits of $3 on each pair of earrings and $5 on each necklace, and she plan to sell at least 30 pieces of jewelry, how can she maximize profit?
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Ticket Out The Door
Work through Ingrid’s optimization problem on the worksheet!
Turn in your worksheet on the back table.
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HOMEWORK
Lesson 3.3Pg. #’s 14, 16, 17, 20, 23, and 24