Graphing Systems of Inequalities: Finding Feasible Regions

Quiz
•
English, Mathematics
•
9th Grade
•
Hard
Anthony Clark
FREE Resource
10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A farmer has 100 acres of land. He wants to plant corn and wheat. Each acre of corn requires 2 hours of labor, and each acre of wheat requires 1 hour of labor. If he has a total of 120 hours of labor available, write a system of inequalities to represent the feasible region for the number of acres of corn (x) and wheat (y) he can plant. Graph the inequalities and identify the feasible region.
The system of inequalities is: { x + y <= 100, 2x + y <= 120, x >= 0, y >= 0 }.
x + 2y <= 100
x + y >= 100
2x + y >= 120
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A school is organizing a field trip and has a budget of $500. The cost per student for the trip is $20, and the bus rental costs $200. Write a system of inequalities to represent the number of students (x) that can attend the trip. Graph the inequalities and determine the feasible region for the number of students.
x >= 0 and x <= 15
x >= 5 and x <= 20
x >= 0 and x <= 10
x >= 0 and x <= 20
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A company produces two types of gadgets: A and B. Each gadget A requires 3 hours of assembly and each gadget B requires 2 hours. The company has a maximum of 30 hours available for assembly. Additionally, they want to produce at least 5 gadgets A. Write a system of inequalities to represent the situation and graph the feasible region.
3x + 2y ≤ 25, x ≥ 5, x ≥ 0, y ≥ 0
2x + 3y ≤ 30, x ≥ 5, x ≥ 0, y ≥ 0
3x + 2y ≤ 30, x ≥ 5, x ≥ 0, y ≥ 0
3x + 2y ≤ 30, x ≥ 3, x ≥ 0, y ≥ 0
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 2 pounds of flour and each vanilla cake requires 1 pound. The bakery has 20 pounds of flour available. If they want to make at least 5 chocolate cakes, write a system of inequalities and graph the feasible region.
2x + y >= 20, x <= 5, x >= 0, y >= 0
x + y <= 20, x >= 5, y >= 0
The system of inequalities is: 2x + y <= 20, x >= 5, x >= 0, y >= 0.
2x + y <= 15, x >= 5, y >= 0
5.
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. The gym wants to earn at least $1,000 in membership fees each month. Write a system of inequalities to represent the number of basic (x) and premium (y) memberships sold. Graph the inequalities and identify the feasible region.
30x + 50y = 1000, x >= 0, y >= 0
The system of inequalities is: 30x + 50y >= 1000, x >= 0, y >= 0.
30x + 50y <= 1000, x >= 0, y >= 0
20x + 40y >= 1000, x >= 0, y >= 0
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A local theater has 200 seats. They sell tickets for $10 for adults and $5 for children. They want to make at least $1,500 from ticket sales. Write a system of inequalities to represent the number of adult (x) and child (y) tickets sold. Graph the inequalities and determine the feasible region.
x + y = 200, 10x + 5y = 1500
x + y ≤ 150, 10x + 5y ≥ 2000
x + y ≤ 200, 10x + 5y ≥ 1500
x + y ≥ 200, 10x + 5y ≤ 1500
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A charity event is planning to sell two types of items: T-shirts and mugs. Each T-shirt costs $15 and each mug costs $10. They want to raise at least $1,200. Additionally, they can only produce a maximum of 100 items. Write a system of inequalities and graph the feasible region for the number of T-shirts (x) and mugs (y) they can sell.
x + y >= 100
x <= 0, y <= 0
The system of inequalities is: 15x + 10y >= 1200, x + y <= 100, x >= 0, y >= 0.
15x + 10y <= 1200
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