Mastering Graphing Inequalities: Feasible Regions Challenge

A farmer has a rectangular field that he wants to fence. The length of the field must be at least 20 meters and the width must be at least 15 meters. Graph the inequalities that represent the dimensions of the field and identify the feasible region.

• L <= 20 and W <= 15

• L >= 15 and W >= 10

• L < 20 and W < 15

• The feasible region is defined by the inequalities L >= 20 and W >= 15.

A school is planning to organize a sports event. They can accommodate at most 200 students and at least 50 students. If each student requires 2 square meters of space, graph the inequality representing the number of students and the area needed, and identify the feasible region.

• The feasible region is defined by the inequalities 100 ≤ x ≤ 150 and A ≥ x, with the area ranging from 200 to 300 square meters.

• The feasible region is defined by the inequalities 50 ≤ x ≤ 200 and A ≥ 2x, with the area ranging from 100 to 400 square meters.

• The feasible region is defined by the inequalities 0 ≤ x ≤ 300 and A ≥ 3x, with the area ranging from 150 to 600 square meters.

• The feasible region is defined by the inequalities 25 ≤ x ≤ 250 and A ≥ 4x, with the area ranging from 50 to 800 square meters.

A company produces two types of gadgets, A and B. Each gadget A requires 3 hours of labor and gadget B requires 2 hours. The company has a maximum of 30 hours of labor available. Graph the inequality representing the production limits and identify the feasible region.

• 3x + 2y ≤ 30, feasible region is below the line in the first quadrant.

• 2x + 3y ≤ 30

• x + y ≤ 15

• 3x + 2y ≥ 30

A restaurant has a budget of $500 for purchasing ingredients. If the cost of ingredient X is $5 per unit and ingredient Y is $10 per unit, graph the inequalities that represent the budget constraints and identify the feasible region.

• x + y ≤ 50

• 5x + 10y = 500

• The feasible region is defined by the inequalities 5x + 10y ≤ 500, x ≥ 0, and y ≥ 0.

• 5x + 10y ≥ 500

A charity organization is collecting donations. They need at least $3000 to fund their project. If they receive $50 from individual donors and $100 from corporate sponsors, graph the inequalities representing the donation amounts and identify the feasible region.

• 50x + 100y ≥ 5000; Feasible region is above the line y = (5000 - 50x) / 100 in the first quadrant.

• 50x + 100y ≤ 3000; Feasible region is below the line y = (3000 - 50x) / 100 in the first quadrant.

• 50x + 100y ≥ 3000; Feasible region is above the line y = (3000 - 50x) / 100 in the first quadrant.

• 50x + 100y = 3000; Feasible region is the area to the left of the line y = (3000 - 50x) / 100 in the first quadrant.

A clothing store sells shirts and pants. Each shirt costs $20 and each pair of pants costs $30. The store wants to make at least $600 in sales. Graph the inequality representing the sales goal and identify the feasible region.

• The inequality is 20x + 30y >= 600, and the feasible region is the area above and including the line 20x + 30y = 600.

• The inequality is 20x + 30y > 600, and the feasible region is the area below and excluding the line 20x + 30y = 600.

• The inequality is 20x + 30y = 600, and the feasible region is the area to the left of the line 20x + 30y = 600.

• The inequality is 20x + 30y <= 600, and the feasible region is the area below the line 20x + 30y = 600.

A local gym has a maximum capacity of 100 members. If they currently have 40 members, how many new members can they accept? Graph the inequality representing the maximum number of new members and identify the feasible region.

• 80

• 60

• 70

• 50

A car rental company has a fleet of cars. They can rent out a maximum of 50 cars per day. If they currently have 20 cars rented, graph the inequality representing the maximum number of additional cars that can be rented and identify the feasible region.

• x <= 20

• x <= 40

• x <= 30

• x <= 10

A bakery sells cakes and cookies. Each cake costs $15 and each cookie costs $2. The bakery wants to earn at least $200 in one day. Graph the inequality representing the earnings goal and identify the feasible region.

• 15x + 2y ≥ 200

• 20x + y ≥ 200

• 10x + 5y ≥ 200

• 15x + 2y ≤ 200

A tech company is developing two products, X and Y. Each product X requires 4 hours of development and product Y requires 3 hours. The team has a maximum of 36 hours available for development. Graph the inequality representing the development time and identify the feasible region.

• The inequality is 4x + 3y ≤ 30, and the feasible region is the area under the line in the second quadrant.

• The inequality is 4x + 3y ≤ 36, and the feasible region is the area under the line in the first quadrant.

• The inequality is 4x + 3y = 36, and the feasible region is the area to the left of the line in the first quadrant.

• The inequality is 4x + 3y ≥ 36, and the feasible region is the area above the line in the first quadrant.