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Linear Programming and Systems of Inequalities

Authored by Anthony Clark

Mathematics

9th Grade

CCSS covered

Linear Programming and Systems of Inequalities
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10 questions

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1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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)

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

It requires that each variables to be greater than or equal to zero

maximization

minimization

inequality

non-negativity constraints

Tags

CCSS.8.EE.C.8B

3.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

4.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

x = 0, y = 300

x = 150, y = 150

x = 100, y 150

x = 150, y = 100

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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).

6.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

(7,4)

(3,10)

(10,1)

(8,5)

7.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

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