Constraints System of Linear Inequalities

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

Which of the following inequalities matches the given graph?

• x ≥ -1

• x ≤ -1

• x > -1

• x < -1

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

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
f(x , y) = 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).

It is a method for finding a maximum or minimum value of some quantity, given a set of constraints.

• Operations research

• Maximization

• Minimization

• Linear programming

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The profit the farmer makes by earning $4,000 for every acre of soybeans he plants and $3,000 for every acre he plants with barley can be modeled by P=4000x+3000y .  If x represents acres of soybeans and y represents acres of corns, which inequalities represent the possible solutions to her situation?

• x≥0
  y≥0
  x+y≥6 
  3x+2y≥15

• x≥0 
  y≥0 
  x+y≤6
  2x+3y≤15

• x≥0 
  y≥0 
  4000x+y≤6
  2x+600y≤15

• P=4000x+3000y

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week.

Which inequality represents the situation?

• x + y ≤ 8

• x + y > 8

• 2x + 3y ≤ 6

• x + y ≤ 10

It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?

• 2x + 3y ≤ 18

• x + y ≤ 6

• x + y ≤ 9

• 3x + 2y ≤ 18

Solve each of the following systems of linear inequalities a graphing approach. Verify using a graphing calculator. Which of following are the corner points?

• (2, 0), (4, 5), (6, 0)

• (2, 0), (3, 5), (0, 6)

• (0, 2), (3.5, 4.5), (6, 2)

• (0, 0), (3, 5), (6, 0)