App- Chapter 5, 6, 7 & 8 - YEAR 12 WORK PDF

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YEAR 12 WORK...

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Question 1

(11 marks)

Consider the project network graphed below.

(a)

Complete the table showing the tasks, the immediate predecessors and the duration of each task. (4 marks)

Task

Immediate Predecessors

Duration (hours)

A B C D E F G H I J K L

(b)

Determine the minimum completion time.

(2 marks)

(c)

List the critical path.

(1 mark)

2

(d)

What is the maximum number of hours that Task A can be delayed so that it does not change the minimum completion time? (1 mark)

(e)

If task B is done immediately, how many hours can J be delayed so as to not necessarily change the critical path? (1 mark)

(f)

State the float time for Task G.

(2 marks)

3

Question 2

(8 marks)

Bakey McBakery produces different types of pies. They have three different ovens that can be used (A, B and C) and four bakers available to operate them. The names of the bakers are Dab, Grug, Bobbin and Salty. An oven will be assigned to a baker for the entire working day. Consider the table shown below. It shows the number of pies that can be baked in a day by each baker. Bakers

Oven

(a)

Dab

Grug

Bobbin

Salty

A

210

180

210

190

B

150

100

140

160

C

170

90

200

180

Draw the weighted bipartite graph below, showing the possible allocations for each of the bakers. (2 marks)

The owner of the company wants to allocate the bakers to the ovens so that the production for a day is the largest amount of pies possible. Having studied Maths Applications in Year 12 at school, the owner decides to solve the problem using the Hungarian Algorithm. (b)

The first step is to transfer the information into a square matrix. Complete the final row. (1 mark)

210 180 210 190 150 100 140 160   170 90 200 180    .... .... .... .... 

4

(c)

Continue the steps of the Hungarian algorithm. Complete the table at the bottom of the page to show the allocation of bakers to ovens that would produce the maximum number of pies for a day. (4 marks)

Baker

Dab

Grug

Bobbin

Salty

Oven (d)

What is the maximum number of pies that can be produced in one day?

5

(1 mark)

Question 3

(3 marks)

Consider the diagram below. It shows the traffic flow (in hundreds of cars) through a road network.

State the capacities of the three cuts.

END OF SECTION 1 6

MATHS APPLICATIONS YEAR 12 TEST 3 2019 Name :

SECTION 2

_____________________________________

Question 4

(5 marks)

Three surgeons (A, B and C) belong to the same private medical practice and need to travel to operate in three different rural hospitals (1, 2 and 3). The doctors will go to one of the hospitals each. The costs involved in travelling to the hospitals, in dollars are shown in the table below.

1 2 3

A 450 620 590

B 400 600 580

C 500 650 570

(a)

If “ABC” represents the situation that Dr A travels to Hospital 1, Dr B travel to Hospital 2 and Dr C travels to Hospital 3, list all of the possible options to allocate each doctor to a particular hospital. (2 marks)

(b)

Hence, which doctor should be allocated to which hospital in order to minimise the total travel costs? (3 marks)

7

Question 5

(11 marks)

Deb has decided to book a three person “makeover team” to come and re-do the interior design of her home. The table below shows the activities that Deb requires the team to complete (in hours) and the immediate predecessors for each activity. Activity

A

B

C

D

E

F

G

H

J

Time (hours)

4.5

4

5

3.5

3.5

4.5

5

6

5

Immediate Predecessors

-

-

A

A

B

C

B

D,F,G

H

(a)

Complete the network diagram below, showing all tasks and durations.

(3 marks)

(b)

Determine the critical path and the minimum completion time for the project.

(2 marks)

(c)

Calculate the float time for (i)

Activity H

(1 mark)

(ii)

Activity E

(1 mark)

8

(d)

(e)

The designers start work at Deb’s place at 7am. (i)

Determine the latest starting time for Activity B.

(1 mark)

(ii)

Determine the earliest start time for Activity G.

(1 mark)

One of the designers is called away to a different job and is unable to work at Deb’s house at all. How, if at all, will this affect the minimum completion time for this project? Explain your answer. (2 marks)

9

Question 6

(5 marks)

The following working shows the use of the Hungarian Algorithm to solve the problem of allocating three workers (W1, W2 and W3) to three tasks (T1, T2 and T3) in the shortest amount of total time. Times are given in minutes. T1

T2

T3

W1

65

20

65

W2

20

10

10

W3

70

30

60

65 20 65  20 10 10   70 30 60 45 0 45  10 0 0     40 0 30  35 0 45 0 0 0   30 0 30  5 0 15 0 30 0    0 0 0 

(a)

What is the minimum total amount of time that the workers could be allocated to the tasks? (1 mark)

(b)

List all possible ways that the tasks could be allocated to the workers in order to achieve this minimum time? (4 marks)

END OF TEST 10...