PROBLEM SOLVING AND GRAPH THEORY.

1. NETWORKING

You are accustomed to everyday traffic and the hustle with buses, maxis and taxis as you travel through-out the country.

Determine all the routes to get from Costaatt South Campus to Costaatt City Campus in Port of Spain and assign weights to each connection between transit points according to

• Distance

• Time

• Money

Clearly identify what the assigned weight measures ( distance, time or cost) and the context in which the routes were chosen for example highways, the oceans or main roads may have been chosen.

You must then do one of the following.

(1) Draw a table showing the connections between each pair of transit points

(2) Da weighted graph to show all possible routes to get from Costaatt South Campus to Costaatt City Campus Port of Spain.

(3) Use Dijkstra’s Algorithm to find the shortest path which would determine the shortest ( time or distance) / cheapest cost to make the journey . In your answer identify the route and the amount.

2. SCHEDULING

Design a project for example tiling a yard, planning a birthday party, designing a website or repainting a car. You need to complete this project in a particular time frame. As you plan your project, aim to maximize your workers, complete the task in the shortest possible time and reduce idle time to a minimum. For your chosen project please do the following:

(1) Create a task table with the headings

• Task i.e. A,B,C, etc.

• Task Description i.e. pick up trash, put gas in tank, or shampoo and condition hair etc.

• Preceding Event i.e. what tasks needs to be done before task A or B etc.

(2) Draw a diagraph to represent this information. Please ensure arrows, task names and duration are correctly placed on the drawing.

(3) Schedule the task using 3 processors and determine the finishing time and idle time if any.

3. PROJECT OUTLINE.

For your chosen questions above in Networking and Scheduling please do the following:

Use a Polya’s Four Step Method for Problem Solving to outline your strategy to solve the problem and hence your solution.

Your outline must have the Following Headings:

i. UNDERSTAND THE PROBLEM

Under this heading you must define the problem. After doing this you need to ask yourself the questions

• What information do I have?

• What information do I need?

• What am I asked to find?

List the answers to these questions in a systematic way so you are directed to use particular strategies to devise a plan. This is the second stage.

ii. DEVISE A PLAN.

• As stated in the textbook there are many ways to attack a problem, therefore you need to ask yourself the questions.

• What is appropriate for your problem e.g. is a weighted graph needed? Or maybe a diagraph? Or a table? You may use other problem solving strategies as discussed in the textbook.

• What techniques will be involved as you work through your problem?

• Again List the answers to these questions in a way that can keep you in the right direction.

iii CARRY OUT THE PLAN.

• The best advice for this area is stated in the textbook. Please make note of any ‘dead ends’ or ‘unforeseen roadblocks’ that you encountered as you persevered to a solution.

• Under this heading you must lay out the explanations for workings and calculations. This area must be detailed and clear for any audience to understand.

iv LOOK BACK AND CHECK.

• As stated in the textbook ‘Check’ your answer to see that it is reasonable and therefore ask yourself the following questions:

Does your answer satisfy the conditions of the problem?

Have you answered all the questions that the problem asks?

Is it possible to solve the problem a different way and get the same result?

Under this heading you need to explain the results obtained in terms of how reasonable etc.

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