Linear Inequality Graphing Solutions with Two Variables

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

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Which system of inequality 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 + 4

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 ≤ 6

• 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

Given the objective function: P = 30x + 50y

Which vertex maximizes the profit?

• (0,0)

• (6,2)

• (8,0)

• (0,6)

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

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 she plants and $3,000 for every acre she 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

Set of all points that satisfy all of the problem's resource restrictions

• extreme points

• intercepts

• feasible region

• graphical solution

When graphing an inequality that has no equals sign (like y > 3x), for the boundary we use

• A dashed line

• A solid line

• A purple line

• The line can't be graphed.

When graphing an inequality that has an equals sign (like y ≥ 4x + 2), for the boundary we use

• A dashed line

• A solid line

• A purple line

• The line can't be graphed.