Linear Inequalities and Systems of Inequalities and Linear Programming

When graphing an inequality, you use a dotted line when you use which symbol?

• <, >

• ≤, ≥ 

Which point is a solution?

• (0, 6)

• (-3, 4)

• (1, 0)

• (-4, 3)

Is (0,0) a solution to the system?

• Solution

• Not a solution

When graphing constraints, what do you call the area where all the shading overlaps?

• the answer

• the feasible region

• the void

• the objective function

Solve the system of inequalities. The feasible region is shown by the darkest blue shading.

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Which of the following inequalities matches the given graph?

• y ≤ -3/4 x + 3

• y ≥ -3/4 x + 3

• y < -3/4 x + 3

• y > -3/4 x + 3

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 system of inequalities matches the graph?

• y > 2x - 4
  y < 2

• y < 2x - 4
  y < 2

• y > 2x - 4
  y <  2 

• y < 2x - 4
  y <   -2

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

In other words...what are the vertices of the feasible region?

• (0, 0), (0, 6), (6, 2), (8, 0)

• (0, 0), (6, 0), (2, 6), (0, 8)