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Maximizing Resources: Linear Inequalities & Feasible Regions

Authored by Anthony Clark

English, Mathematics

9th Grade

Maximizing Resources: Linear Inequalities & Feasible Regions
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10 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A farmer has 100 meters of fencing to create a rectangular pen for his sheep. If the length of the pen is represented by x and the width by y, write the inequality that represents the maximum area of the pen. What is the feasible region for the dimensions of the pen?

x + y <= 50, x >= 0, y >= 0

x + y >= 50, x >= 0, y >= 0

x + y <= 100, x >= 0, y >= 0

x + y <= 50, x < 0, y >= 0

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A school is planning a field trip and has a budget of $500. The cost per student is $20 for transportation and $15 for admission. Write an inequality to represent the maximum number of students that can attend the trip. Identify the feasible region for the number of students.

x ≤ 20

x ≤ 10

x ≤ 14

x ≤ 12

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A factory produces two types of toys: type A and type B. Each type A toy requires 2 hours of labor and each type B toy requires 3 hours. If the factory has 60 hours of labor available, write the inequality that represents the production limits. What is the feasible region for the number of toys produced?

2x + 3y ≥ 60

3x + 2y ≤ 60

x + 2y ≤ 60

2x + 3y ≤ 60

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A gym offers two types of memberships: basic and premium. The basic membership costs $30 per month, and the premium membership costs $50 per month. If a customer wants to spend no more than $200 on memberships, write an inequality to represent this situation. What is the feasible region for the number of each type of membership?

30x + 50y = 200, x ≥ 0, y ≥ 0

30x + 50y < 200, x ≥ 0, y ≥ 0

30x + 50y ≤ 250, x ≥ 0, y ≥ 0

30x + 50y ≤ 200, x ≥ 0, y ≥ 0

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 3 cups of flour and each vanilla cake requires 2 cups. If the bakery has 24 cups of flour, write the inequality that represents the maximum number of cakes that can be made. Identify the feasible region for the number of cakes.

3x + 2y ≤ 24

2x + 3y ≤ 24

4x + y ≤ 24

x + 4y ≤ 24

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A concert hall has a seating capacity of 300. If tickets for the front row cost $50 and tickets for the back row cost $30, and the total revenue must be at least $10,000, write an inequality to represent this situation. What is the feasible region for the number of tickets sold?

x + y ≤ 250, 50x + 30y ≥ 12000

x + y ≥ 300, 50x + 30y ≤ 10000

x + y = 300, 50x + 30y = 10000

x + y ≤ 300, 50x + 30y ≥ 10000

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A company produces two products, A and B. Each product A requires 4 hours of machine time and each product B requires 2 hours. If the company has 40 hours of machine time available, write the inequality that represents the production limits. Identify the feasible region for the number of products produced.

3x + 2y ≤ 40

4x + 2y ≥ 40

4x + 3y ≤ 40

4x + 2y ≤ 40

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