Mastering Graphing Linear Inequalities and Feasible Regions

A farmer has a rectangular field. The length of the field is 3 meters more than twice the width. If the width must be at least 4 meters, graph the inequality and identify the feasible region for the dimensions of the field.

• The feasible region is defined by w >= 5 and l = 2w + 5.

• The feasible region is defined by w <= 4 and l = 2w - 3.

• The width must be at least 6 meters and l = 2w + 1.

• The feasible region is defined by w >= 4 and l = 2w + 3.

A school is planning a field trip and has a budget of $500. The cost per student is $20, and the total number of students must be less than or equal to 30. Write the inequality for the number of students and graph it to find the feasible region.

• x <= 25

• x >= 20

• x <= 30

• x < 25

A company produces two types of gadgets, A and B. Each gadget A requires 2 hours of labor, and each gadget B requires 3 hours. If the company has a maximum of 12 hours of labor available, graph the inequality and identify the feasible region for the number of gadgets produced.

• The feasible region is defined by the inequality 2x + 3y = 12.

• The feasible region is defined by the inequality 2x + 3y ≤ 12, including the axes and the line segment from (0,4) to (6,0).

• The feasible region is defined by the inequality x + y ≤ 12.

• The feasible region is defined by the inequality 2x + 3y ≥ 12.

A local bakery can produce a maximum of 100 loaves of bread and 80 pastries in a day. If each loaf of bread requires 1 hour of work and each pastry requires 0.5 hours, graph the inequalities and identify the feasible region for the daily production.

• x <= 80, y <= 100, and x + 0.5y <= 100

• x <= 50, y <= 40, and x + 0.5y <= 60

• The feasible region is defined by the inequalities x <= 100, y <= 80, and x + 0.5y <= 80.

• x <= 120, y <= 90, and x + 0.5y <= 100

A gym has a maximum capacity of 50 members. If each member pays $30 per month, and the gym wants to earn at least $1200 per month, write the inequality for the number of members and graph it to find the feasible region.

• 40 <= x <= 50

• 30 <= x <= 40

• x < 30

• x > 50

A pet store sells cats and dogs. Each cat costs $100 and each dog costs $200. If the store wants to make at least $1000 in sales, graph the inequality and identify the feasible region for the number of cats and dogs sold.

• The feasible region is defined by the inequality 100x + 200y = 1000, graphed in the third quadrant.

• The feasible region is defined by the inequality 100x + 200y ≥ 1000, graphed in the first quadrant.

• The feasible region is defined by the inequality 100x + 200y ≤ 1000, graphed in the second quadrant.

• The feasible region is defined by the inequality 100x + 200y ≥ 500, graphed in the first quadrant.

A concert venue has a seating capacity of 200. If tickets for the concert are sold at $15 each, and the venue wants to earn at least $1500, write the inequality for the number of tickets sold and graph it to find the feasible region.

• 100 ≤ x ≤ 200

• 50 ≤ x ≤ 150

• 200 < x ≤ 250

• x < 100

A clothing store has a sale on shirts and pants. Each shirt costs $25 and each pair of pants costs $40. If the store wants to sell at least $1000 worth of clothing, graph the inequality and identify the feasible region for the number of shirts and pants sold.

• The feasible region is defined by the inequality 25x + 40y ≤ 1000 in the first quadrant.

• The feasible region is defined by the inequality 25x + 40y = 1000 in the second quadrant.

• The feasible region is defined by the inequality 25x + 40y ≥ 500 in the first quadrant.

• The feasible region is defined by the inequality 25x + 40y ≥ 1000 in the first quadrant.

A community center has a budget of $3000 for a new playground. If swings cost $150 each and slides cost $200 each, write the inequality for the number of swings and slides that can be purchased and graph it to find the feasible region.

• 150x + 200y < 3000

• 150x + 200y = 3000

• 100x + 250y ≤ 3000

• 150x + 200y ≤ 3000

A charity organization is planning a fundraiser. They want to sell tickets for a dinner event at $50 each. If they want to raise at least $2000, graph the inequality for the number of tickets sold and identify the feasible region.

• x ≥ 40

• x ≤ 40

• x < 40

• x > 40