Systems of Linear Inequalities Feasible Regions

What do you call the area where all the shading overlaps?

• the answer

• the feasible region

• the void

• the objective function

Which are the vertices of the feasible region?

• (0, 0), (0, 6), (6, 2), (8, 0)
• (0, 0), (6, 0), (2, 6), (0, 8)

The corners of a feasible region are (-3,3), (-2,6), (0,6), and (1.5,3). The objective function is: P = 4x - 2y. Find the maximum and minimum values of the function for this region.

• The maximum value is 0 at (0, 6). The minimum value is - 20 at (-3, 3).

• The maximum value is 0 at (-3, 3). The minimum value is - 20 at (0, 6).

• The maximum value is 0 at (-2, 6). The minimum value is - 20 at (1.5, 3).

• The maximum value is 0 at (1.5, 3). The minimum value is - 20 at (-2, 6).

Find the values of x and y that maximize the objective function P = 3x + 2y for the graph. What is the maximum value?
   

• maximum value at (5, 4); 32
• maximum value at (0, 8); 16
• maximum value at (9, 0); 27
• maximum value at (0, 0); 0

Which of the graphs shows the correct feasible region for this system of inequalities?

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• 100

• 550

• 600

• 300

Graph the system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the function for this region. 3 ≤ y ≤ 6 y ≤ 3x + 12 y ≤ -2x + 6

P = 4x - 2y

• The maximum value is 0 at (0, 6). The minimum value is - 20 at (-3, 3).
• The maximum value is 0 at (-3, 3). The minimum value is - 20 at (0, 6).
• The maximum value is 0 at (-2, 6). The minimum value is - 20 at (1.5, 3).
• The maximum value is 0 at (1.5, 3). The minimum value is - 20 at (-2, 6).