Linear Programming — Test Answers

1

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Which graph represents the solution to the system of inequalities?

A

On a coordinate plane, a curve approaches the x-axis in quadrant 2 and increase through (0, 1) and (2, 9). An ellipse has center (0, 0) and goes through (4, 0), (0, negative 8), (negative 4, 0), and (0, 8). Everything inside of the ellipse and below the curve is shaded.

B

On a coordinate plane, a curve approaches the x-axis in quadrant 2 and increase through (0, 1) and (2, 9). An ellipse has center (0, 0) and goes through (4, 0), (0, negative 8), (negative 4, 0), and (0, 8). Everything inside of the ellipse and above the curve is shaded.

C

On a coordinate plane, a curve approaches the x-axis in quadrant 2 and increase through (0, 1) and (2, 9). An ellipse has center (0, 0) and goes through (8, 0), (0, negative 4), (negative 8, 0) and (0, 4). Everything inside of the ellipse and below the curve is shaded.

D

Option

2

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During free play, there must be more than 4 campers in a group, and the number of boys must not exceed the number of girls by more than 5. Which graph represents this system of inequalities?

A

Option

B

Option

C

Option

D

Option

3

Dwayne is selling hamburgers and cheeseburgers. He has 100 burger buns. Each hamburger sells for $3, and each cheeseburger sells for $3.50. Which system of inequalities represents the number of hamburgers, h, and the number of cheeseburgers, c, he must sell to have sales of at least $80?

A

h + c ≤ 803h + 3.5c ≤ 100

B

h + c ≤ 803h + 3.5c ≥ 100

C

h + c ≤ 1003h + 3.5c ≤ 80

D

h + c ≤ 1003h + 3.5c ≥ 80

4

The system of inequalities in the graph represents the change in an account, y, depending on the days delinquent, x.

A

≤

B

≥

C

<

D

>

5

Which ordered pairs are in the solution set of the system of linear inequalities?y > x + 2y < 2x + 3

A

(2, 2), (3, 1), (4, 2)

B

(2, 2), (3, –1), (4, 1)

C

(2, 2), (1, –2), (0, 2)

D

(2, 2), (1, 2), (2, 0)

6

The members of the drama club have 100 tickets to sell to the school play. Students pay $5 per ticket, and nonstudents pay $10 per ticket. The drama club needs to collect at least $800 in total ticket sales. The system of inequalities represents the number of student tickets, s, and the number of nonstudent tickets, n, the members must sell. s + n ≤ 1005s + 10n ≥ 800

A

40

B

60

C

80

D

100

7

A salad made such that the difference between twice the ounces of greens and the ounces of carrots is at least 3. Also, the sum of the ounces of greens and twice the ounces of carrots is less than 4. Which graph represents the system of equations for this scenario?

A

Option

B

Option

C

Option

D

Option

8

Review the graph.

A

y ≤ x2 – 8 and x > y2 + 1

B

y ≥ x2 – 8 and x < y2 + 1

C

y ≤ x2 + 1 and x > y2 – 8

D

y ≥ x2 + 1 and x < y2 – 8

9

Which is true about the solution to the system of inequalities shown?y > 3x + 1y < 3x – 3

A

Only values that satisfy y > 3x + 1 are solutions.

B

Only values that satisfy y < 3x – 3 are solutions.

C

Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.

D

There are no solutions.

10

On a coordinate plane, 2 dashed straight lines are shown. The first line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything to the right of the line is shaded. The second line has a negative slope and goes through (negative 2, 0) and (2, negative 4). Everything to the right of the line is shaded.

A

y > x + 1

B

y < x – 1

C

y > x – 1

D

y < x + 1

11

Which statements are true about the graph of the system of linear inequalities? Select two options.y > 3x – 4y < x + 1

A

The graph of y > 3x − 4 has shading above a dashed line.

B

The graph of y < x + 1 has shading below a dashed line.

C

The graphs of the inequalities will intersect.

D

There are no solutions to the system.

E

The graphs of the two inequalities intersect the y-axis at (0, 1) and (0, 4).

12

Which graph represents the solution of x2 + (y – 2)2 8x?

A

On a coordinate plane, a circle has center (0, 2) and radius 3. A parabola opens to the right and goes through (8, 8), has vertex (0, 0), and goes through (4, negative 6). Everything inside of the circle and inside of the parabola is shaded.

B

On a coordinate plane, a circle has center (0, 2) and radius 3. A parabola opens to the right and goes through (8, 8), has vertex (0, 0), and goes through (4, negative 6). Everything inside of the circle and outside of the parabola is shaded.

C

On a coordinate plane, a circle has center (2, 0) and radius 6. A parabola opens to the right and goes through (8, 8), has vertex (0, 0), and goes through (4, negative 6). Everything inside of the circle and outside of the parabola is shaded.

D

Option

13

A pair of weak earthquakes is modeled by a system of inequalities. One earthquake occurred roughly 20 km east and 14 km north of the center of Columbia, NC. The quake could be felt from 25 km away. A couple days later, another earthquake occurred 8 km west and 3 km north of the center of Columbia and could be felt from 14 km away. If Columbia is located at (0, 0) on a coordinate grid, the system of inequalities represents this scenario.

A

4 km west and 12 km south

B

6 km west and 4 km north

C

2 km east and 10 km north

D

6 km east and 8 km north

Linear Programming — Test Answers

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