Free Printable Linear Programming

1.

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week.
Which inequality represents the situation?

a)

x + y ≤ 8

b)

x + y ≤ 6

c)

2x + 3y ≤ 6

d)

x + y ≤ 10

2.

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?

a)

2x + 3y ≤ 18

b)

x + y ≤ 6

c)

x + y ≤ 9

d)

3x + 2y ≤ 18

3.

Sarah makes $30 for each small purse (x) and $50 for each big purse (y). What is the objective quantity?

a)

P = 30x + 50y

b)

P = 50x + 30y

4.

Objective quantity:
P = 30x + 50y
Corner that maximizes profit: (0, 6)
What is the profit?

a)

300

b)

280

c)

400

d)

240

5.

Which of the following inequalities matches the given graph?

a)

x ≥ -1

b)

x ≤ -1

c)

x > -1

d)

x < -1

6.

Which of the following inequalities matches the given graph?

a)

y ≤ -3/4 x + 3

b)

y ≥ -3/4 x + 3

c)

y < -3/4 x + 3

d)

y > -3/4 x + 3

7.

Which are vertices of the feasible region?

a)

(0, 3) (3, 0) (5, 8)

b)

(0, 6) (3, 5) (6, 5)

c)

(3, 3) (8, 5) (5, 8)

d)

(0, 5) (6, 0) (3, 3)

8.

What do you call the area where all the shading overlaps?

a)

the answer

b)

the feasible region

c)

the void

d)

the objective function

9.

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

Which vertex maximizes the profit?

a)

(0,0)

b)

(6,2)

c)

(8,0)

d)

(0,6)

10.

Find the values of x and y that maximize the objective function P = 3x + 2y for the graph. What is the maximum value?

a)

maximum value at (5, 4); 32

b)

maximum value at (0, 8); 16

c)

maximum value at (9, 0); 27

d)

maximum value at (0, 0); 0

11.

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?

a)

x≥0

y≥0

x+y≥6

3x+2y≥15

b)

x≥0

y≥0

x+y≤6

2x+3y≤15

c)

x≥0

y≥0

4000x+y≤6

2x+600y≤15

d)

P=4000x+3000y

12.

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 . What is the maximum profit that she can earn?

a)

$15,000

b)

$21,000

c)

$18,000

d)

$25,000

13.

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 . What combination of soybeans and corn will maximize profit?

a)

4 acres of soybeans and 2 acres of corn

b)

6 acres of soybeans and 0 acres of corn

c)

3 acres of soybeans and 3 acres of corn

d)

0 acres of soybeans and 5 acres of corn

14.

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

x+y\le8

5x-7y\ge-14

y\ge2

a)

(2, 0), (4, 5), (6, 0)

b)

(2, 0), (3, 5), (0, 6)

c)

(0, 2), (3.5, 4.5), (6, 2)

d)

(0, 0), (3, 5), (6, 0)

15.

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

a)

b)

c)

d)

16.

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

a)

extreme points

b)

intercepts

c)

feasible region

d)

graphical solution

17.

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

a)

maximization

b)

minimization

c)

inequality

d)

non-negativity constraints

18.

In the graph, this is the intercept when the value of x = 0

a)

x - intercept

b)

y - intercept

c)

vertex

d)

first quadrant

19.

In the graph, this is the intercept when the value of y = 0

a)

x - intercept

b)

y - intercept

c)

vertex

d)

first quadrant

20.

Which system of inequality is shown?

a)

y ≥ -x - 1
y < x + 4

b)

y < -x - 1
y ≥ x + 4

c)

y > -x - 1
y ≥ x + 4

d)

y > -x - 1
y ≥ x + 4

Linear Programming

Total questions: 20

Worksheet time: 42mins

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