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Formulation of Mathematical Equations

Introduction to Formulation of Mathematical Equations

When formulating a formula, it is important that the model has some of the first principles and there is an event that can be used as an example to verify. One also needs to understand the structure and the make of the event or occurrence that owner is trying to model that will help with the different variables that are allowed by mathematical models. One should always ask oneself if this is a natural phenomenon, if the event is expected to be continuous, and if yes, how would it be continuous, will the formula allow conclusion even if it is not completely accurate. Without these questions, there are many mathematical models which could be very much compatible with the data collected. If the data at hand is simple, use simple models. There are sometimes other methodologies that one can use to choose the best models such as Fourier analysis regression analysis or fitting analysis. In a general modelling problem, one would say that some variables represent something (Thomas, 2015).

The Plan for Formulation of Mathematical Equations

From the national quality framework, the ratio of educators to children is 1:4 for 0-35 months and 1:11 for 36 months and above. Using this data, less than 35 months old are in room1-3. The data in room 1 is 9, in room two is 7, 12 in room 3, 12 in room 4 and 9 in room 5. In room one, on Monday the organization will need two educators, in room 2, the organization will also need 2 educators, in room 3, there is a need of three educators, in room 4, they will need 1 educator same as in room 5. Total educators on Monday will be 9 educators.

In formulating an equation that will help in determining the number of educators in response to the number of children that are available for that day, I would create variables in a way that I would say that;

 From the information given and data collected, my decision variable will be X1 for children below 3 years, X2 being children above 3 years, and Y1 being educators with diploma qualification, Y2  being educators with certificate qualifications and W being educators from the agency.

Constraints are the rules enforced on a data column of a table limiting the type of data that can be entered in a table. There are two types of constraints, a column constraint and a table constraint. A column constraint applies to one column whereas a table constraint applies to the whole table. A non-negative constraint is constraints that cannot be negative. In our case, we cannot have negative constraints as we are dealing with people and we cannot have negative people.

An objective function is the function in which its valuables need to be minimized of increased.

 Following the data given, it can be assumed that;

On Monday, the total number of children under 35 months was 28 and the total number of children above 35 months is 21. Following the equation generated above, we can say that;

Y=x/4 and y=a/11

Y=28/4 which is 7

Y= 21/11 which is 1.9 rounding up to the nearest whole number is 2

The total number of educators needed for Monday would be 9. Seven to be in children below 35 months old and the rest are in children over 35 months of age.

Following the schedule of the organization’s educators, I would draft the below table (Yaromir, 2014)

Days and room

1

2

3

4

5

Monday

Educator1,10

Educator 7, 6

Educator 11,14 and 5

Educator 15

Educator 4

Tuesday

Educator1,10 and 2

Educator 7, 6 and 3

Educator11,14,5 ,16

Educator15

Educator4

Wednesday

Educator 1,10

Educator 7,6,3

Educator11,14,5,16

Educator15

Educator4,5

Thursday

Educator1,10

Educator7, 6

Educator 11,14, 5

Educator 15

Educator4

Friday

Educator1,10

Educator7,6

Educator 11,14, 5

Educator15

Educator4,

The cost of this plan will involve the cash payable to educators who are qualified as diplomas and certificate. There were no educators that were hired from the agency hence no expenses by the agency.

From the table above, we have 8 diploma educators each working for 8 and a half hour daily for 5 days at a rate of 27.55 USD per hour. This results to a total of 9367USD and 3 educators who have certificate qualification are paid at a rate of 24.22USD giving a total of 2724.75 USD. The total amount to be spent by the organization is the summation of the total amount payable as per that week which is estimated to be 12091.75USD.

Following the ratio of educators and children given by the national quality framework, there are days when educators have fewer children available hence more children can be added as there is room available, for instance, rooms that can be available on Monday is room 5 for two children and room 2 for 1 child. On Tuesday, there is no room for any other child in any room. On Wednesday, there is one vacancy in room 2, on Thursday, there is a vacancy in room 4 and on Friday, there is a vacancy in room 5 and room2.

References for Formulation of Mathematical Equations

Thomas, W. M. (2015). Methods of mathematical modelling. Cham: SPringer.

Yaromir, T. (2014). Linear programing: theory, algorithms and applications. New Yock: Nova Science Publishers.

Remember, at the center of any academic work, lies clarity and evidence. Should you need further assistance, do look up to our Supply Chain Management Assignment Help

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