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.

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

3.

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)

4.

Write the system of inequalities
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing.

a)

x+y≤300
7.5x+5.5y≥2000

b)

x+y<300
7.5x+5.5y≥2000

c)

x+y≤300
7.5x+5.5y≤2000

d)

x+y>2000
7.5x+5.5y≤300

5.

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

a)

300

b)

280

c)

400

d)

240

6.

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

7.

Rachel owns a car and a moped. She has at most 12 gallons of gas to be used between the car and the moped. The car's tank holds at most 10 gallons and the moped's 3 gallons. The mileage for the car is 20 mpg and for the moped is 100 mpg.
What are the constraints?

a)

x≤10, y≤3, x+y≤12

b)

0≤x≤10, 0≤y≤3, x+y≤12

c)

x≥0, y≥0, 10x+3y≤12

d)

x≤10, y≤3, 10x+3y≤12

8.

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

9.

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

a)

b)

c)

d)

10.

x + 3 ≤ 4y

a)

b)

c)

d)

11.

Trees in urban areas help keep air fresh by absorbing carbon dioxide. A city has RM2100 to spend on planting spruce and maple trees. The land available for planting is 45,000 square feet. Plant a spruce costs RM30 and plant a maple tree costs RM40. A spruce requires an area of 600 square feet and a maple tree requires an area of 900 square feet. A spruce absorbs 650 pounds of carbon dioxide per year and a maple tree absorbs 300 pounds of carbon dioxide per year. (Let x the spruce and y the maple tree). Write and objective function and constraints for a linear program that models the situation. Simplify the inequalities.

a)

b)

c)

d)

12.

If the given inequality is greater than or greater than or equal, the region _______________ the straight line ax+by+c=0 has to be shaded.

a)

below

b)

above

13.

To find the optimal solution for maximum cases, all entries in the objective row of the final tableau are ___________

a)

positive

b)

negative

14.

2x + 9 ≥ 3y

a)

b)

c)

d)

15.

A manufacturing company makes two types of television sets; one is black and white (x) and the other is colour (y). The company has resources to make at most 300 sets a week. It takes Rs 1800 to make a black and white set and Rs 2700 to make a coloured set. The company can spend not more than Rs 648000 a week to make television sets. Constraints are

a)

$x+y\le300,\ 2x+3y\le720$

b)

$x+y\le300,\ 2x+3y\ge720$

c)

$x+y\ge300,\ 2x+3y\le720$

d)

$x+y\ge300,\ 2x+3y\ge720$

16.

Which graph represents:

3x+5y\le15000

3x+16y\ge24000

y\le x

a)

b)

c)

d)

17.

Find the optimal point and optimal value with the objective "minimise $G=3x+4y$ "

a)

Optimal point: $\left(63\frac{8}{11},32\frac{7}{11}\right)$
Optimal value: $321\frac{8}{11}$

b)

Optimal point: $\left(100\frac{4}{5},\ 16\frac{4}{5}\right)$
Optimal value: $369\frac{3}{5}$

c)

Optimal point: $\left(63\frac{7}{11},32\frac{8}{11}\right)$
Optimal value: $321\frac{9}{11}$

d)

Optimal point: $\left(100\frac{4}{5},\ 16\frac{4}{5}\right)$
Optimal value: $321\frac{2}{5}$

18.

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

a)

(0, 0), (0, 6), (6, 2), (8, 0)

b)

(0, 0), (6, 0), (2, 6), (0, 8)

19.

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

20.

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

a)

300

b)

280

c)

400

d)

240

Linear Programming

Total questions: 20

Worksheet time: 40mins

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