Graphing Linear Inequalities: Find the Feasible Regions

A farmer has a rectangular field. The length must be at least 10 meters and the width must be at least 5 meters. Graph the inequalities that represent the possible dimensions of the field. What is the feasible region?

• The feasible region is the area in the first quadrant bounded by L >= 10 and W >= 5.

• The feasible region is the area in the third quadrant bounded by L >= 5 and W >= 10.

• The feasible region is the area in the first quadrant bounded by L < 10 and W < 5.

• The feasible region is the area in the second quadrant bounded by L <= 10 and W <= 5.

A school is planning a fundraiser. They need to sell at least 200 tickets and can sell a maximum of 500 tickets. Graph the inequalities for the number of tickets sold. Identify the feasible region.

• The feasible region is the area between the lines y = 100 and y = 600.

• The feasible region is the area between the lines y = 200 and y = 500, inclusive.

• The feasible region is the area below the line y = 200.

• The feasible region is the area above the line y = 500.

A factory produces two types of gadgets. The production of type A must be at least 50 units and type B must not exceed 100 units. Graph the inequalities and identify the feasible region for production.

• A >= 100 and B <= 50

• A < 50 and B > 100

• A <= 50 and B >= 100

• The feasible region is defined by A >= 50 and B <= 100.

A gym has a capacity limit of 150 members. If they currently have 80 members, how many new members can they accept? Graph the inequality and identify the feasible region for new memberships.

• 100

• 30

• 70

• 50

A restaurant can serve a maximum of 300 meals per day. If they serve at least 100 meals for lunch, how many can they serve for dinner? Graph the inequalities and identify the feasible region.

• D can be at most 200 meals for dinner.

• D can be at most 150 meals for dinner.

• D can be at most 250 meals for dinner.

• D can be at most 100 meals for dinner.

A charity event requires at least 30 volunteers and can accommodate a maximum of 60 volunteers. Graph the inequalities and identify the feasible region for volunteer participation.

• v > 60

• v = 45

• v < 30

• The feasible region for volunteer participation is 30 <= v <= 60.

A local park has a limit of 200 visitors at any time. If there are already 120 visitors, how many more can enter? Graph the inequality and identify the feasible region for visitor entry.

• 80

• 60

• 100

• 150

A concert venue can hold a maximum of 500 people. If 200 tickets are sold, how many more can be sold? Graph the inequality and identify the feasible region for ticket sales.

• 100

• 250

• 300

• 400

A company produces two products. The production of product X must be at least 30 units and product Y must not exceed 70 units. Graph the inequalities and identify the feasible region for production.

• The feasible region is defined by x <= 30 and y >= 70.

• The feasible region is defined by x >= 50 and y <= 50.

• The feasible region is defined by x <= 30 and y <= 70.

• The feasible region is defined by the area where x >= 30 and y <= 70.

A sports team needs at least 15 players to form a team and can have a maximum of 25 players. Graph the inequalities and identify the feasible region for team formation.

• 10 <= x <= 20

• 15 < x < 30

• The feasible region for team formation is 15 <= x <= 25.

• x < 15 or x > 25