3.3 Optimization with Linear Programming

It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?

• 2x + 3y ≤ 18
• x + y ≤ 6
• x + y ≤ 9
• 3x + 2y ≤ 18

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

Which of the following inequalities matches the given graph?

• x ≥ -1
• x ≤ -1
• x > -1
• x < -1

Tags

CCSS.HSA.REI.D.12

Which of the following inequalities matches the given graph?

• y ≤ -3/4 x + 3
• y ≥ -3/4 x + 3
• y < -3/4 x + 3
• y > -3/4 x + 3

Tags

CCSS.HSA.REI.D.12

What do you call the area where all the shading overlaps?

• the answer

• the feasible region

• the void

• the objective function

Tags

CCSS.HSA.REI.D.12

x + 3y - 6 ≥ 0

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Tags

CCSS.HSA.REI.D.12

y > 2

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Tags

CCSS.HSA.REI.D.12

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Which are vertices of the feasible region?

• (0, 3) (3, 0) (5, 8)

• (0, 6) (3, 5) (6, 5)

• (3, 3) (8, 5) (5, 8)

• (0, 5) (6, 0) (3, 3)

Tags

CCSS.HSA.REI.D.12

Given the objective function: P = 30x + 50y

Which vertex maximizes the profit?

• (0,0)

• (6,2)

• (8,0)

• (0,6)

Tags

CCSS.HSA.REI.D.12

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.10

Find the values of x and y that maximize the objective function P = 3x + 2y for the graph. What is the maximum value?
   

• maximum value at (5, 4); 32
• maximum value at (0, 8); 16
• maximum value at (9, 0); 27
• maximum value at (0, 0); 0

Tags

CCSS.HSA.REI.D.12

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Solve the system of inequalities. The feasible region is shown by the darkest blue shading.

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Tags

CCSS.HSA.REI.D.12