Name: ________________________ Class: ___________________ Date: __________ ID: A

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Unit 06-05 - Sytems of Linear Inequalities

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. Identify the inequality that represents the graph:

a. y 2x 3 c. y 2x 3

b. y 2x 2 d. y 3x 2

____ 2. Identify the inequality that represents the graph:

a. y 2

3 x 3 c. y 2

3 x 2

b. y 3

2 x 2 d. y 3

2 x 3

Name: ________________________ ID: A

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____ 3. Graph the solutions of the linear inequality: 8x 2y 6

a. c.

b. d.

Name: ________________________ ID: A

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____ 4. Graph the system of linear inequalities: 3x 2y 6

4x 3y 6

Ï

ÌÓ

ÔÔÔÔÔÔÔÔÔÔ

a. c.

b. d.

____ 5. A cabinet maker is required to make at least 4 large cabinets each week. He is not required to make any small cabinets.

It takes 5 hours to build a large cabinet and 4 hours to build a small cabinet. The cabinet maker has no more than 40 hours to build cabinets each week.

Let x represent the number of large cabinet and y represent the number of small cabinets.

Write a system of constraints to represent this situation.

a. x 4

y 0

5x 4y 40

c. x 4

y 0

5x 4y 9

b. x 0

y 4

5x 4y 40

d. x 1

y 5

5x 4y 9

Name: ________________________ ID: A

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____ 6. A cabinet maker is required to make at least 4 large cabinets each week. He is not required to make any small cabinets.

It takes 5 hours to build a large cabinet and 4 hours to build a small cabinet. The cabinet maker has no more than 40 hours to build cabinets each week.

Let x represent the number of large cabinet and y represent the number of small cabinets.

If there is a $50 profit on the large cabinets and a $30 profit on the small cabinets. What number of large and small cabinets maximizes the objective function?

P 50x 30y

a. 4 large and 0 small c. 4 large and 5 smallb. 8 large and 0 small d. 0 large and 10 small

____ 7. A company produces mopeds and motorcycles. It must produce at least 10 mopeds per month. The company has the equipment to produce at most 60 mopeds. It can also produce at most 120 motorcycles. The productions of mopeds and motorcycles cannot exceed 160.

The profit on a moped is $134 and on a motorcycles is $200. Use the graph of the feasible region to determine the maximum profit the company can generate.

a. $25,340 c. $12,000b. $29,360 d. $32,040

Name: ________________________ ID: A

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____ 8. A company is building Laptops. The deluxe model takes 3 hours to produce and a basic model that takes 1 hour to produce. They have enough supplies to make 1000 laptops and 1600 hours of labor.

Let x represent the number of deluxe models and y represent the number of basic laptops.

Write a system of constraints to represent this situation.

a. x 0

y 0

3x 1y 1000

x y 1600

c. x 0

y 0

3x 3y 1600

x y 1000

b. x 0

y 0

3x 1y 1600

x y 1000

d. x 0

y 0

x 3y 1600

x y 1000