Benchmark1 Review
1. Connecting Flights between cities are shown in the vertex edge graph below. A represents Atlanta B represents Boston,
C represents Chicago, D represents Denver and F represents Fort Lauderdale.
Create a vertex edge graph that represents the matrix above:
Use matrices C,D,E,F,G and H to find the following. If the Matrix does not exist , write impossible.
2.
3.
4. Using the system
and the function
Solve the system by graphing.
Name the vertices of the polygonal convex set.
Find the minimum and maximum values of the function.
y
7
6
5
4
3
2
1
–7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
5.Represent the graph with nodes A,B, C , D using a matrix. (vertex-edge graph)
1 2 3 4 5 6 7
x
A
B
C
D
6. Represent the graph with nodes A,B, C , D using a matrix. (vertex-edge graph)
A
B
C
F
D
Write a system of Equations to represent the situation then solve.
7. The senior classes at Luella and Woodland planned separate trips to Disneyworld. At Luella they rented and filled 6 van
and 3 buses with 201 students. At Woodland they rented and filled 8 van and 6 buses with 334 students. How many can a
van carry? How many can a bus carry?
8. Flying to Atlanta with a tailwind a plane averaged 206 km/h. on the return trip the plane only averaged 106km/h while
flying back in the same wind. Find the speed of the wind and the speed of the plane still in the air.
9. Find the solution of the system of equations.
10. What equations can be used to solve for x and y?
Given :
11. Find A — B
12. Find 2A+B
13. Give the associated matrix for the vertex-edge graph shown:
14. Find the solution of the system of equations.
15. Find the minimum and maximum values of the objective
function for the given feasible region, using
y
45
40
35
30
(0, 28)
(16, 25)
25
20
15
10
5
(0, 0)
5
(50, 0)
10 15 20
25 30 35 40
45 50 55
60
x
.
16. Which has a larger area?
Triangle ABC: A(13,6) B(–5,2) C (–19,7) OR Triangle DEF: D(–13,6) E (5,2) C(–19,7)
17. Find the minimum and maximum values of the objective function subject to the given constraints:
Objective Function
Constraints
18. Find the minimum and maximum values of the objective function for the given feasible region, using
.
y
(–27, 18)
(6, 11)
x
(25, –25)
(–6, –27)
19. A farmer has 90 acres available for planting millet and alfalfa. Seed costs $4 per acre for millet and $6 per acre for
alfalfa. Labor costs are $20 per acre for millet and $10 per acre for alfalfa. The expected income is $110 per acre for
millet and $150 per acre for alfalfa. The farmer intends to spend no more than $480 for seed and $1400 for labor.
Graph the feasible region. What is the maximum income for the given constraints?
20.The Northern Wisconsin Paper Mill can convert wood pulp to either notebook paper or newsprint. The mill can
produce, at most, 200 units of paper a day. At least 10 units of notebook paper and 80 units of newsprint are required
daily by regular customers. The profit on a unit of notebook paper is $500 and the profit on a unit of newsprint is $350.
Graph the feasible region. What is the maximum income for the given constraints?
Benchmark1 Review
Answer Section
MULTIPLE CHOICE
1. ANS: D
STA: MM3A7a
SHORT ANSWER
2. ANS:
STA: MM3A4a(multiply)
3. ANS:
STA: MM3A4a(multiply)
4. ANS:
y
7
6
5
4
3
2
1
–7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
1 2 3 4 5 6 7
x
Vertices:( 0,0) (2,0) (0 , 4) ( 4, 4)
The maximum is 10
The minimum is –16
5. ANS:
STA: MM3A7b
6. ANS:
STA: MM3A7b
7. ANS:
A van can carry 17 students and a bus can carry 33 students.
8. ANS:
plane speed= 156
wind speed = 50
9. ANS:
10. ANS:
11. ANS:
STA: MM3A4a(subtract)
12. ANS:
STA: MM3A4a(add) MM3A4a(scalar)
13. ANS:
14. ANS:
x = 14.5, y = 18, z = –1
15. ANS:
The minimum value is 0 and the maximum value is 1,110.
16. ANS:
Triangle ABC is larger
17. ANS:
The minimum value is 0 and the maximum value is 48.
18. ANS:
The minimum value is –279 and the maximum value is 465.