Question 4-Mine Workers' Transport Vehicle Problem

Workplace’s activity: Mine Workers' Transport Vehicle Problem

Question 4    

A mine workers' transport vehicle can carry 36 workers. All workers need to be transported to the mine daily across a 90 minutes periods: 6.30-8.00 in the morning, and 4.00-5.30 in the afternoon. The round trip takes 15 minutes. If 1134 workers need to be transported every day, morning and evening, how many vehicles would be required assuming the mine vehicles are the only option for workers to get to the worksite?

A- Solution

My working on this question includes three steps through two parts: Part 1 is my Planning, and Part 2 is my Action.

PART 1- PLANNING

My aim is to plan a procedure of steps to find out three key features of 
*the total number of round trips needed, 
*the maximum number of trips that a vehicle can transport/operate within 90 minutes, and 
*the minimum number of vehicles which are needed to transport all mine workers to the mine worksite.

These features will be determined through the procedure of three steps as below.
 
Step 1-Finding the total number of round trips needed
In this first session of Step 1, I consider knowing and working out the total number of round trips, also called trips in this activity, which are required/needed to transport all mine workers to the worksite.

Step 2- Finding the maximum number of trips that a vehicle could operate/transport within 90 minutes.
In this second session of Step 2, after knowing the total trips needed from Step 1, I consider knowing and working out the maximum number of trips that a vehicle could transport within 90 minutes.

Step 3- Finding the minimum number of vehicles needed.
In the final session of Step 3, I consider finding out the minimum number of vehicles that is required/needed to achieve all trips (which found at Step 1).

With this planning, my Action concentrating on three steps above will be illustrated in next part.

PART 2- ACTION 
Based on three steps above, in this Part 2, my detailed approach and calculations are as below.

Let's start
Step 1

The total number of trips = 1134 workers ÷ 36 workers per trip = 32 trips.

(Note: 31 trips with full 36 workers, and 1 trip with 18 workers. This may develop further interesting things such as rearrangements of numbers of workers between vehicles).

At this point, I may find real objects representing for 32 trips. For example, I would collect 32 wooden sticks, and put each stick representing one trip. 

Step 2

The maximum number of trips that a vehicle could transport within 90' = 90' ÷ 15' = 6 trips. 
I have set that one stick stands for one trip. So with six trips that a vehicle can operate/transport, it needs six sticks.
In other words, at this stage, I know that for each vehicle, I need six sticks standing for six trips. It means that 6 sticks are the maximum numbers which can be put in one group representing one vehicle.

Step 3

The minimum number of vehicles needed = (1) ÷  (2) =  32 trips ÷ 6 trips = 6 vehicles.

This result is found by putting 32 the wood sticks in groups of 6. 

A reminder here: each group of 6 sticks is to represent one vehicle with the maximum of 6 trips [each stick stands for one trip].

As a result, I need 6 vehicles. Now I can visually realize that the vehicles from #1 to #5 will operate/transport 6 trips, and the vehicle #6 will operate/transport 2 trips only. See the image below.

                                   

Because the last group #6 or the last vehicle #6 has only 2 sticks or 2 trips, therefore, from this point, I can play some games by moving the sticks around, to make new decisions. This allows and opens new options in scheduling to manage the vehicles and their trips. For example, if moving one stick from vehicle #1, one stick from vehicle #2 and put them to vehicle #6, then the numbers of trips operating by the vehicle #1 are now reduced to 5 trips; the numbers of trips operating by vehicle #2  are also reduced to 5 trips; but the numbers of trips operating by the vehicles #6   are now increased to 4 trips;

Further from this point, for example, if in the morning session, the vehicle #3 operated all 6 trips, then in the afternoon session, I would reduce the number of trips for this vehicle. This would create a better working environment in terms of reducing stress levels for both drivers and mine workers.

In conclusion, the minimum of six (6) vehicles would be required assuming the mine vehicles are the only option for workers to get to the worksite.

--

My Notes
*These mine workers need time to get on and get off the vehicles. This factor, of loading and unloading workers, is ignored in this activity. In reality, time for loading and unloading needs to be considered.



*I've found that this question is very interesting since it develops more issues to think about, particularly, the management matter. 

B-A collection of peers' feedback

 

This task is also posted on 
*my google site Learning Teaching Adult Numeracy in VET at https://sites.google.com/site/lydiale2016eeb308csu/how-many-they-would-be-required;

and more detailed information can be viewed @
*my Learning and Teaching Blog at http://lydialeeleuts.blogspot.com.au/2016/08/using-sticks-in-solving-numeracy-problem.html

Question 1-Fibonacci's Rabbit Problem

Fibonacci’s rabbit problem

1-How many pairs of rabbits will there be after a year if it is assumed that every month each pair produces one new pair, which begins to bear two young two months after its own birth? Assume we start the year with one newborn pair.

A-Solution:

In solving this problem, I believe that understanding the Fibonacci's sequence, and applying techniques of determining boundaries of the start and the end of rabbits' identification hold extremely important roles. My work divides finding information into two main steps as below.

Step 1-Understanding of Fibonacci Number, or Fibonacci's sequence.

It is crucial to understand the notion of Fibonacci Number or Fibonacci's sequence.

This Fibonacci’s sequence can be illustrated in an image as below. 

AboutEducation-Russell (2016) considers this sequence is a recursive sequence.
In practice, it is obviously that the Fibonacci's sequence formula is used to determine a series of numbers in which each current or given number is the sum of the two numbers preceding it.
In my work for this problem, these two numbers namely the first predecessor, and the second predecessor. Setting the 'n' as the current or given number, then its first predecessor number is 'n-1', and its second predecessor number is 'n-2'. Traditionally, as mentioned, the Fibonacci's sequence formula is expressed as follows.                                                       F(n)=F(n-1)+F(n-2)

This formula will be used to find out numbers of pairs of rabbits. These rabbits need to be identified at the start and at the end of each month, in the following step.

Step 2-Setting and determining the boundaries towards the identification of rabbits. 

The identity of rabbits is crucial in a process of finding the numbers of rabbits. This process begins with a setting to determining the pivotal points of boundaries. According to Walker (2013)  'boundaries identify where something starts and where something ends, and anything that has no Boundary has no identity’. Therefore, I believe that one core activity of this exercise is to set and determine the boundaries by determining the start and the end of the boundaries between months when the rabbits are identified for their identities. In other words, the boundaries of this exercise refer to the points of the start and the end of each month where all pairs of rabbits need to be counted.

My application of the 'Walker's boundaries ' to identify Fibonacci's rabbits is as follows:

Let's set:

F0 = Month (0) ==> starts with a rabbit baby pair

F1 = Month (1) ==> continues with a rabbit youth pair

F2 = Month (2) ==> continues with a rabbit adult pair

F(n) = Month (n) 

In this case, Fibonacci’s [sequence] numbers occur from F3 , i.e [Fibonacci] Month(3).

Each subsequent number is the sum of the two preceding it. Using Microsoft Excel is my tool to find the figures as below.

                    

In adding images of Adult, Baby, and Youth rabbits into my Microsoft Excel 2013 file, and using its relevant functions for calculating and drawing, my figures of pairs of rabbits for each month and the end of 12 months are visually and mathematically calculated, found and illustrated as follows.

The information above shows that after a year, there will be 233 [89+89+55] pairs[i.e. 466] of rabbits including 89 adult pairs, 89 baby pairs, and 55 youth pairs.

Therefore, there will be 233 pairs of rabbits after a year. 

My notes: 

Arguably, this question has being embedded the absurdity of real life, therefore it causes to raise further questions and problems since it has been called so. In addition, the question guides and focuses on the Fibonacci's sequence dealing with a single influence of the Fibonacci's issue. In fact, I believe that if at the beginning, the boundary's notion is provided and considered, then the solution can be easily found, and this Fibonacci's issue would no longer be problem.
However, I believe that with raising viewpoints from different edges of an issue will help learners gain more knowledge and develop their critical thinking skills.

 

B-A collection, from the CSU's discussion forum, of peers' feedback and my reflection 

 

This task is also posted on   
 *my Learning and Teaching blog at http://lydialeeleuts.blogspot.com.au/2016/07/fibonaccis-rabbit-problem.html

and more detailed information can be viewed at

 *my google site Learning Teaching Adult Numeracy in VET at https://sites.google.com/site/lydiale2016eeb308csu/fibonacci-s-rabbit-problem;