Real-Life Linear Inequalities: Exploring Feasible Regions

A local bakery can produce a maximum of 200 loaves of bread per day. If they want to produce at least 50 loaves of whole grain bread, how many loaves of white bread can they make? Write an inequality to represent this situation and identify the feasible region.

• x + y ≤ 200, y ≥ 50; feasible region: 0 ≤ x ≤ 150, y ≥ 50.

• x + y = 200, y ≥ 50; feasible region: 0 ≤ x ≤ 200, y ≥ 50.

• x + y ≥ 200, y ≤ 50; feasible region: 0 ≤ x ≤ 100, y ≤ 50.

• x + y ≤ 150, y ≥ 50; feasible region: 0 ≤ x ≤ 100, y ≥ 50.

A school is planning a field trip and has a budget of $1,200. Each student ticket costs $15, and the bus rental costs $300. Write an inequality to represent the maximum number of students that can attend the trip and identify the feasible region.

• x ≤ 50

• x ≤ 30

• x ≤ 60

• x ≤ 75

A farmer has 100 acres of land and wants to plant corn and wheat. Each acre of corn requires 1 hour of labor, and each acre of wheat requires 2 hours. If the farmer has 120 hours of labor available, write an inequality to represent the situation and identify the feasible region.

• x + y <= 100, x + 2y >= 120

• x + y <= 100, x + 2y <= 120

• x + y <= 80, x + 2y <= 100

• x + y >= 100, x + 2y >= 120

A gym has a maximum capacity of 150 members. If they currently have 80 members, how many new members can they accept while staying within capacity? Write an inequality and identify the feasible region.

• 80

• 70

• 60

• 100

A concert venue can hold a maximum of 500 people. If 200 tickets have already been sold, how many more tickets can be sold? Write an inequality to represent this situation and identify the feasible region.

• 250

• 300

• 400

• 100

A company produces two types of gadgets: Type A and Type B. Each Type A gadget requires 3 hours of labor, and each Type B gadget requires 2 hours. If the company has 30 hours of labor available, write an inequality to represent the maximum number of each type of gadget that can be produced and identify the feasible region.

• x + y ≤ 15

• 3x + 2y < 30

• 3x + 2y ≥ 30

• 3x + 2y ≤ 30

A charity event aims to raise at least $5,000. If each ticket sold is $25, how many tickets must be sold to meet the goal? Write an inequality and identify the feasible region.

• 250 tickets must be sold.

• At least 200 tickets must be sold.

• 150 tickets must be sold.

• 100 tickets must be sold.

A restaurant has a seating capacity of 120. If they have 40 tables and each table seats 4 people, how many tables can be reserved for a special event while staying within capacity? Write an inequality and identify the feasible region.

• 20

• 50

• 35

• 30

A clothing store has a sale on shirts and pants. If they have 200 shirts and 150 pairs of pants, and they want to sell at least 100 items total, write an inequality to represent this situation and identify the feasible region.

• x + y > 100, x < 200, y < 150

• x + y = 100, x >= 200, y <= 150

• x + y >= 100, x <= 200, y <= 150

• x + y <= 100, x >= 200, y >= 150

A student is saving money for a new laptop that costs $800. If they currently have $200 and save $50 each week, write an inequality to represent how many weeks it will take to save enough money and identify the feasible region.

• w >= 12

• w = 15

• w < 12

• w <= 10