Inequalities and Feasible Regions: Real-World Scenarios

A farmer has 100 meters of fencing to create a rectangular pen for his animals. If the length of the pen is represented by x and the width by y, what inequality represents the maximum area he can enclose?

• x + y < 50

• x + y ≤ 50

• 2x + 2y ≤ 100

• x + 2y ≤ 50

A school is planning a field trip and has a budget of $500. If each student ticket costs $15 and each adult ticket costs $20, write an inequality to represent the number of tickets they can purchase if they want to stay within budget.

• 15x + 20y < 500

• 10x + 15y ≤ 500

• 15x + 20y ≤ 500

• 20x + 15y ≤ 500

A bakery sells cookies for $2 each and muffins for $3 each. If the bakery wants to make at least $100 in one day, write an inequality to represent the relationship between the number of cookies (x) and muffins (y) sold.

• 2x + 3y ≥ 100

• x + y ≥ 50

• 2x + 3y ≤ 100

• 4x + 2y ≥ 100

A concert venue has a maximum capacity of 300 people. If x represents the number of adult tickets sold and y represents the number of child tickets sold, what inequality represents the seating constraint?

• x + y ≥ 300

• x + y = 300

• x + y ≤ 300

• x + y < 300

A local gym has a promotion where they can only accept 50 new members. If x represents the number of adult memberships and y represents the number of student memberships, write an inequality to show the maximum number of memberships they can accept.

• x + y ≤ 50

• x + y ≥ 50

• x + y = 50

• x + y < 50

A pizza shop sells large pizzas for $10 and small pizzas for $6. If they want to earn at least $200 in one day, create an inequality that represents the number of large (x) and small (y) pizzas they need to sell.

• 5x + 8y >= 200

• 10x + 6y < 200

• 10x + 6y >= 200

• 15x + 4y >= 200

A charity event aims to raise at least $1,000. If each ticket sold for adults is $25 and for children is $15, write an inequality to represent the total number of adult (x) and child (y) tickets that need to be sold to meet the goal.

• 25x + 20y ≥ 1000

• 25x + 15y ≥ 1000

• 20x + 10y ≥ 1000

• 30x + 20y ≥ 1000

A company produces two types of gadgets. Each gadget A requires 2 hours of labor and each gadget B requires 3 hours. If the company has 30 hours of labor available, write an inequality to represent the production limits of gadgets A (x) and B (y).

• x + y ≤ 10

• 4x + 2y ≤ 30

• 2x + 3y ≤ 30

• 2x + 3y ≥ 30

A school is organizing a sports day and has a limit of 200 participants. If x represents the number of students participating in track events and y represents those in field events, what inequality represents the total number of participants?

• x + y ≤ 200

• x + y ≥ 200

• x + y = 200

• x + y < 200

A clothing store has a sale where they can only sell a maximum of 150 items. If x represents the number of shirts sold and y represents the number of pants sold, write an inequality to show the maximum number of items they can sell.

• x + y ≤ 150

• x + y = 150

• x + y < 150

• x + y ≥ 150