Bounded and Unbounded Inequalities

the process of finding the maximum or minimum values of a function for a region defined by inequalities

• linear programming

• system of inequalities

• ordered triple

a system of inequalities that forms a region that is open

• unbounded region

• bounded region

• feasible region

A region that is bounded when the graph of a system of constraints is a polygonal region

• bounded region

• feasible region

• unbounded region

For this image, is the solution set bounded or unbounded?

• Bounded, because the graph passes through the origin

• Unbounded, because the graph passes through the origin

• Bounded, because the graph continues forever downwards

• Unbounded, because the graph continues forever downwards

The vertices of a system of equations are shown in the picture.
If the function f(x, y) = -3x + 5y, then what are the minimum and maximum values?

• Maximum = 26, minimum = 10

• Maximum = 50, minimum = 40

• Maximum = 7, minimum = 5

• Maximum = 10, minimum = -6

The feasible region of a graph is the area showing all of the possible points that satisfy the system of inequalities.

What is another name for the feasible region?

• y-intercept

• rise over run

• solution set

• bounded region

Which graph represents the solution set to the system of inequalities?

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A system of inequalities has these vertices:
(-2. 1)
(-4, 3)
(5, 2)
If the solution set is defined by the function f(x, y) = -2x + 3y + 4, then what are the minimum and maximum values?
(Assume the graph has a bounded solution set.)

• Maximum = 3, minimum = -8

• Maximum = 24, minimum = 0

• Maximum = 24, minimum = 11

• Maximum = 11, minimum = 0

Solve the following inequality:

7b - 3 < 11

• b < 2

• 84 > b

• b > 2

• b < 84

Which system of inequalities is shown?

• y ≥ -x - 1
  y < x + 4

• y < -x - 1
   y ≥ x + 4

• y > -x - 1
  y ≥ x + 4

• y > -x - 1
  y ≥ x + 3