Graphing Inequalities: Identifying Feasible Regions in Context

A farmer wants to plant two types of crops, A and B. Crop A requires at least 3 hours of sunlight and 2 units of water per week, while Crop B requires at least 2 hours of sunlight and 3 units of water. Graph the inequalities representing the sunlight and water requirements and identify the feasible region for planting both crops.

• The feasible region is defined by the area where x >= 3 and y >= 3.

• The feasible region is defined by the area where x <= 3 and y >= 3.

• The feasible region is defined by the area where x >= 3 and y <= 2.

• The feasible region is defined by the area where x <= 2 and y <= 2.

A company produces two products, X and Y. Product X requires at least 4 hours of labor and 5 units of raw material, while Product Y requires at least 3 hours of labor and 2 units of raw material. Graph the inequalities for labor and raw material constraints and determine the feasible region for production.

• The feasible region is the area on the graph where the inequalities intersect, representing all possible combinations of products X and Y that can be produced without exceeding labor and raw material limits.

• The feasible region is the area where only product X can be produced.

• The feasible region is determined solely by the labor constraint.

• The feasible region includes all points on the graph without any restrictions.

A school is organizing a field trip and has a budget of $500. The cost per student for transportation is $20 and for food is $15. Graph the inequalities representing the budget constraints and identify the feasible region for the number of students that can attend the trip.

• The maximum number of students that can attend the trip is 14.

• The maximum number of students that can attend the trip is 10.

• The maximum number of students that can attend the trip is 20.

• The maximum number of students that can attend the trip is 18.

A restaurant offers two types of meals, vegetarian and non-vegetarian. The vegetarian meal requires at least 2 vegetables and 1 grain, while the non-vegetarian meal requires at least 1 vegetable and 2 grains. Graph the inequalities for the meal requirements and identify the feasible region for meal preparation.

• The feasible region is defined by the inequalities x >= 2, y >= 1 for vegetarian meals and x >= 1, y >= 2 for non-vegetarian meals.

• The feasible region is defined by the inequalities x >= 3, y >= 2 for vegetarian meals and x >= 0, y >= 1 for non-vegetarian meals.

• The feasible region is defined by the inequalities x >= 1, y >= 1 for vegetarian meals and x >= 2, y >= 2 for non-vegetarian meals.

• The feasible region is defined by the inequalities x >= 2, y >= 0 for vegetarian meals and x >= 1, y >= 3 for non-vegetarian meals.

A manufacturer produces two types of gadgets, G1 and G2. Gadget G1 requires at least 5 hours of assembly and 3 units of battery, while Gadget G2 requires at least 2 hours of assembly and 4 units of battery. Graph the inequalities for assembly and battery constraints and identify the feasible region for production.

• The feasible region is represented by the equation 3x + 2y = B.

• The feasible region is defined by the inequalities 2x + 5y <= A and 4x + 3y <= B.

• The feasible region is defined by the intersection of the inequalities 5x + 2y <= A and 3x + 4y <= B.

• The feasible region is determined solely by the assembly constraint 5x <= A.

A tech company is developing two software applications, App A and App B. App A requires at least 10 hours of coding and 5 hours of testing, while App B requires at least 8 hours of coding and 3 hours of testing. Graph the inequalities for coding and testing hours and identify the feasible region for development.

• The feasible region is defined by the inequalities x >= 10 and y >= 5.

• The feasible region is defined by the inequalities x <= 8 and y <= 3.

• The feasible region is defined by the inequalities x >= 8 and y >= 3.

• The feasible region is defined by the inequalities x <= 10 and y <= 5.

A clothing store sells two types of shirts, casual and formal. Casual shirts require at least 2 yards of fabric and 1 hour of labor, while formal shirts require at least 3 yards of fabric and 2 hours of labor. Graph the inequalities for fabric and labor constraints and identify the feasible region for production.

• The feasible region is the entire graph without any constraints.

• The feasible region is the area on the graph where the inequalities 2x + 3y ≤ F and x + 2y ≤ L intersect, including the axes.

• The feasible region is the area where 3x + 2y ≤ F and 2x + y ≤ L intersect.

• The feasible region is only the area above the axes on the graph.

A gym offers two types of memberships, basic and premium. The basic membership allows for 3 classes per week and costs $30, while the premium membership allows for unlimited classes and costs $50. Graph the inequalities representing the class limits and costs and identify the feasible region for membership sales.

• The feasible region is defined by the inequalities: 0 <= x <= 5 for basic membership and x >= 0 for premium membership, with costs C <= 40 for basic and C <= 60 for premium.

• The feasible region is defined by the inequalities: 0 <= x <= 2 for basic membership and x >= 1 for premium membership, with costs C <= 20 for basic and C <= 45 for premium.

• The feasible region is defined by the inequalities: 0 <= x <= 4 for basic membership and x >= 0 for premium membership, with costs C <= 25 for basic and C <= 55 for premium.

• The feasible region is defined by the inequalities: 0 <= x <= 3 for basic membership and x >= 0 for premium membership, with costs C <= 30 for basic and C <= 50 for premium.

A local bakery produces two types of cakes, chocolate and vanilla. The chocolate cake requires at least 4 eggs and 2 cups of sugar, while the vanilla cake requires at least 3 eggs and 3 cups of sugar. Graph the inequalities for egg and sugar constraints and identify the feasible region for cake production.

• The feasible region is defined by the inequalities 4x + 2y <= total eggs and 3x + 2y <= total sugar.

• The feasible region is determined solely by the chocolate cake constraints.

• The feasible region is defined by the intersection of the inequalities 4x + 3y <= total eggs and 2x + 3y <= total sugar.

• The feasible region includes only the points where x and y are both greater than 5.