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 ≤ 10

b)

x + y ≤ 6

c)

2x + 3y ≤ 8

d)

x + y ≤ 8

2.

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

3.

Objective quantity:

P = 30x + 50y

Corner that maximizes profit: (0, 6)

What is the profit?

a)

240

b)

280

c)

400

d)

300

4.

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

5.

Which graph represents:

3x+5y\le15000

3x+16y\ge24000

y\le x

a)

b)

c)

d)

6.

What is an optimal solution?

a)

The aim of the problem.

b)

Values that satisfy all constrains.

c)

The feasible solution that meets the objective.

d)

The numbers of each of the things that can be varied. The variables, often called x, y, z etc, will be the ‘letters’ in the inequalities and the objective function.

7.

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: $321\frac{2}{5}$

8.

Find the optimal point and optimal value with the objective "maximise $P=2x+y$ "

a)

Optimal point: $\left(37.5,\ 22.5\right)$
Optimal value: $97.5$

b)

Optimal point: $\left(16\frac{2}{3},\ 10\right)$
Optimal value: $43\frac{1}{3}$

c)

Optimal point: $\left(38.5,\ 24.5\right)$
Optimal value: $101.5$

d)

Optimal point: $\left(41.5,\ 25.5\right)$
Optimal value: $105.5$

9.

Maximise cost for the scenario above.

a)

$£161$

b)

$£173$

c)

$£200$

d)

$£163$

Linear Programming

Total questions: 9

Worksheet time: 37mins

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