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 4000x+y≤6 2x+600y≤15

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

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).

What does the shaded region in the graph of a linear inequality represent?

All solutions to the inequality

What does the overlapping region in a system of linear inequalities indicate?

All possible solutions that satisfy all inequalities

Solutions that satisfy only one inequality

Finding Solutions to Linear Inequalities

Authored by Anthony Clark

Mathematics

9th Grade

CCSS covered

Finding Solutions to Linear Inequalities

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18 questions

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

the intersection of the graphs in a system of constraints

feasible region

bounded region

unbounded region

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

MULTIPLE CHOICE QUESTION

1 min • 1 pt

a set of inequalities with the same variables

system of inequalities

system of equations

inconsistent system

DROPDOWN QUESTION

1 min • 1 pt

The ordered pair (a) is in the solution set of 8x+16y>32.

(-3, 5)

(0, 2)

(-1, 1)

(4, 0)

MULTIPLE CHOICE QUESTION

1 min • 1 pt

any of the points of intersection of the graphs of the constraints that determine a feasible region

vertex

ordered triple

bounded region

a system of inequalities that forms a region that is open

unbounded region

bounded region

feasible region

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

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Finding Solutions to Linear Inequalities

the intersection of the graphs in a system of constraints

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

a set of inequalities with the same variables

The ordered pair (a) is in the solution set of 8x+16y>32.

any of the points of intersection of the graphs of the constraints that determine a feasible region

a system of inequalities that forms a region that is open

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?

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

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

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

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