Graphing Inequalities and Linear Functions

The video tutorial explains how to use linear programming to find the maximum value of an objective function subject to constraints. It covers graphing linear inequalities, finding feasible regions, and determining vertices. The tutorial also demonstrates solving a system of equations using elimination and evaluating the objective function at vertices to find the maximum value.

What is the objective function in this linear programming problem?

• Z = 4X + 2Y

• Z = 6X + 17Y

• Z = 7X + 8Y

• Z = 5X + 3Y

Which region is shaded when graphing y >= 0?

• Below the line

• Above the line

• To the left of the line

• To the right of the line

What type of line is used to graph x >= 0?

• Dotted line

• Curved line

• Solid line

• Dashed line

How do you determine the side to shade for the inequality 3x + 5y <= 90?

• By shading neither side

• By guessing

• By using a test point

• By shading both sides

What is the x-intercept of the line 3x + 5y = 90?

• (18, 0)

• (0, 18)

• (30, 0)

• (0, 0)

What is the y-intercept of the line 6x - y = 48?

• (0, -48)

• (8, 0)

• (48, 0)

• (0, 48)

Which point is used as a test point for shading the inequality 6x - y <= 48?

• (2, 2)

• (0, 0)

• (1, 1)

• (3, 3)

What is the intersection point of the lines 6x - y = 48 and 3x + 5y = 90?

• (30, 0)

• (0, 18)

• (10, 12)

• (8, 0)

What is the maximum value of the objective function Z?

• 264

• 48

• 306

• 204

At which point does the maximum value of Z occur?

• (0, 0)

• (8, 0)

• (0, 18)

• (10, 12)