The preparation of a meal requires the completion of all ten activities A to J. The network diagram shows the activities and their completion times in minutes. (a) What is the minimum time needed to prepare the meal? (b) List the activities which make up the critical path for this network. (c) Complete the table below, showing the earliest start time and float time for activities A and G. Activity Earliest start time (minutes) Float time (minutes)

SSCE HSC Mathematics Standard Annuities: The preparation of a meal requir

The preparation of a meal requires the completion of all ten activities A to J - HSC - SSCE Mathematics Standard - Question 26 - 2020 - Paper 1

Question 26

The preparation of a meal requires the completion of all ten activities A to J. The network diagram shows the activities and their completion times in minutes. (a) ... show full transcript

Worked Solution & Example Answer:The preparation of a meal requires the completion of all ten activities A to J - HSC - SSCE Mathematics Standard - Question 26 - 2020 - Paper 1

Step 1

What is the minimum time needed to prepare the meal?

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Answer

To determine the minimum time needed to prepare the meal, we analyze the network diagram by identifying all the paths from start to finish and calculating their total durations. The paths are:

A -> B -> D -> H -> J: 12 + 6 + 8 + 10 + 7 = 43 minutes
A -> C -> E -> H -> J: 12 + 8 + 20 + 10 + 7 = 57 minutes
B -> D -> E -> F -> H -> J: 0 + 8 + 20 + 10 + 7 = 45 minutes
A -> B -> E -> F -> H -> J: 12 + 6 + 20 + 10 + 7 = 55 minutes

After evaluating all paths, the minimum time required is found to be 46 minutes.

Step 2

List the activities which make up the critical path for this network.

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Answer

The activities that make up the critical path are:

C -> D -> E -> F -> H -> I

Step 3

Complete the table below, showing the earliest start time and float time for activities A and G.

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Answer

Activity	Earliest start time (minutes)	Float time (minutes)
A	0	12
G	36	15

The preparation of a meal requires the completion of all ten activities A to J - HSC - SSCE Mathematics Standard - Question 26 - 2020 - Paper 1

Worked Solution & Example Answer:The preparation of a meal requires the completion of all ten activities A to J - HSC - SSCE Mathematics Standard - Question 26 - 2020 - Paper 1

What is the minimum time needed to prepare the meal?

List the activities which make up the critical path for this network.

Complete the table below, showing the earliest start time and float time for activities A and G.

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