Exploring Feasible Regions: Graphing Nonlinear Inequalities

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 inequalities x <= 3, y <= 2, x <= 2, and y <= 3.

• The feasible region is only determined by the sunlight requirements of crop A.

• The feasible region is defined by the intersection of the inequalities x >= 3, y >= 2, x >= 2, and y >= 3.

• The feasible region includes all points where x < 3 and y < 3.

A company produces two products, X and Y. Product X requires 4 hours of labor and 2 units of raw material, while product Y requires 3 hours of labor and 5 units of raw material. If the company has a maximum of 24 hours of labor and 20 units of raw material available, graph the inequalities and determine the feasible region for production.

• The feasible region is the area on the graph where the inequalities intersect, bounded by the axes and the lines 4x + 3y = 24 and 2x + 5y = 20.

• The feasible region is the area where the lines 4x + 5y = 24 and 2x + 3y = 20 intersect.

• The feasible region is the entire area under the axes without any boundaries.

• The feasible region is defined only by the line 4x + 3y = 24 without considering raw material constraints.

A restaurant offers two types of meals, vegetarian and non-vegetarian. The vegetarian meal requires 1 hour of preparation and 2 ingredients, while the non-vegetarian meal requires 2 hours of preparation and 3 ingredients. If the restaurant has 10 hours of preparation time and 15 ingredients available, graph the inequalities and find the feasible region for meal preparation.

• The feasible region is defined by the vertices (0,4), (4,0), (2,3), and (1,5).

• The feasible region is defined by the vertices (1,1), (0,7), (7,0), and (4,3).

• The feasible region is defined by the vertices (0,0), (0,5), (5,0), and (3,2).

• The feasible region is defined by the vertices (2,2), (0,6), (6,0), and (3,1).

A local gym offers two types of fitness classes: yoga and spinning. Each yoga class requires 1 hour and 2 participants, while each spinning class requires 2 hours and 3 participants. If the gym has a maximum of 10 hours and 15 participants available, graph the inequalities and identify the feasible region for class scheduling.

• The feasible region is defined by the inequalities 1x + 2y <= 10 and 2x + 3y <= 15, with x >= 0 and y >= 0.

• The feasible region is defined by the inequalities 1x + 2y <= 15 and 2x + 3y <= 10, with x >= 0 and y >= 0.

• The feasible region is defined by the inequalities 2x + 2y <= 10 and 1x + 3y <= 15, with x >= 0 and y >= 0.

• The feasible region is defined by the inequalities 1x + 3y <= 10 and 2x + 2y <= 15, with x >= 0 and y >= 0.

A manufacturer produces two types of gadgets, A and B. Each gadget A requires 2 hours of assembly and 1 unit of material, while each gadget B requires 1 hour of assembly and 2 units of material. If the manufacturer has 12 hours of assembly time and 10 units of material, graph the inequalities and determine the feasible region for production.

• 2x + y >= 12, x + 2y >= 10

• The feasible region is defined by the inequalities 2x + y <= 12, x + 2y <= 10, x >= 0, and y >= 0.

• x + y <= 12, 2x + y <= 10

• x >= 2, y >= 1

A tech company is developing two software products, A and B. Product A requires 5 hours of coding and 3 hours of testing, while product B requires 2 hours of coding and 4 hours of testing. If the company has a maximum of 30 hours of coding and 20 hours of testing available, graph the inequalities and find the feasible region for product development.

• The feasible region is defined by the inequalities 2x + 5y <= 30 and 4x + 3y <= 20.

• The feasible region is defined by the inequalities 5x + 2y <= 20 and 3x + 4y <= 30.

• The feasible region is defined by the inequalities 5x + 4y <= 30 and 3x + 2y <= 20.

• The feasible region is defined by the inequalities 5x + 2y <= 30 and 3x + 4y <= 20, along with x >= 0 and y >= 0.

A clothing store sells two types of shirts, casual and formal. Each casual shirt requires 2 yards of fabric and 1 hour of labor, while each formal shirt requires 3 yards of fabric and 2 hours of labor. If the store has 20 yards of fabric and 15 hours of labor available, graph the inequalities and identify the feasible region for shirt production.

• The feasible region is bounded by the lines 2x + 3y = 20 and x + 2y = 15, along with the axes x = 0 and y = 0.

• The feasible region is bounded by the lines 3x + 2y = 20 and x + y = 15.

• The feasible region is bounded by the lines 2x + 3y = 15 and x + 2y = 20.

• The feasible region is bounded by the lines 2x + 2y = 20 and x + y = 15.

A bakery produces two types of cakes, chocolate and vanilla. Each chocolate cake requires 3 cups of sugar and 2 eggs, while each vanilla cake requires 2 cups of sugar and 3 eggs. If the bakery has 18 cups of sugar and 12 eggs available, graph the inequalities and determine the feasible region for cake production.

• The feasible region is defined by the vertices (0,0), (0,4), (6,0), and (3,2).

• The feasible region for cake production is defined by the vertices (1,1), (5,0), (0,4), and (3,3).

• The feasible region is defined by the vertices (0,0), (0,5), (3,0), and (4,2).

• The feasible region for cake production is defined by the vertices (0,0), (0,6), (4,0), and (2,3).