University : Middle East College UniLearnO is not sponsored or endorsed by this college or university.
Subject Code : MASC20004
Assignment Task :

Module Learning Outcomes
The following LOs are achieved by the student by completing the assignment successfully
1)
Construct and solve Linear Programming models.
2) Construct and test statistical hypotheses.

 

Assignment Objective
1.
To test the understanding and application of Mathematical concepts learning.
2. To test the calculation skills and Mathematical modelling ability of the learner.
3. To test the knowledge acquired by the learners on using statistical test and ability to infer on the outcomes.

Assignment Tasks
Use the suitable resources to find the solution of the following problems.
Assignment questions
1.
Trace the history of Operations research ( Quantitative method). Define linear programming model, and briefly explain its assumptions, limitations and scope to various industries. 
2. Assume that you are planning to open a perfume shop by taking loan from bank. The shop requires a minimum of carpet area of 25 ????2. The monthly rent for each ????2 is 12 rials per month. Choose any four brands of perfumes you can sell in your shop. A box of 50 bottles in every brand requires 0.25 ????2of carpet area. The purchase cost of 500 bottles of the cheapest brand perfume is equal to two months shop rent. Cost of each next cheapest model brand perfumes are 25% higher than its lower brand cost. Fix the selling price of the cheapest perfume at 20% profit, and the next cheapest models at 15%, 13% and 10% profits respectively. In each of the shops it is known that the showcase area of perfume boxes is at most ten times of the shop carpet area. The bank loan policies allows you to apply a loan upto 500 times of the shop carpet area. In the town, building owners normally build shops with the carpet area 36 ????2 ,49 ????2,64 ????2,81 ????2 and 100 ????2 respectively. You financial conditions allows you to apply a loan upto 42000 rials. Assume that all perfumes are completely sold out at the end of each month. Formulate the above case as a linear programming problem

 

3. There are two cake factories located one at Al Khoud and the other at Bawsher area. From these locations, cakes are to be delivered to other three outlet shops located at Mutrah, Barka and Nizwa. The weekly demand at these outlets are 5, 5 and 4 units while the production capacity of the factories at 8 and 6 units respectively. The cost of transportation per unit is given below

Muttrah

 

How many units should be transported from each factory to each outlet in order to reduce the transportation cost. Formulate the above problem as a linear programming problem and solve it with a suitable method.
Explain the solution briefly. 
 

4. Solve the following simplex problem using suitable slack, surplus and Artificial variables.

Unrestricted

 

5. Assume the Covid-19 Pandemic across the globe in 2019-2020 and you are doing a research based on the data of a particular hospital. In this context define and briefly explain the following terms with suitable examples and necessary assumptions.
(a) Null hypothesis and alternate hypothesis.  
(b) Type -1 and Type 2 errors  
(c) Critical region  
(d) Significance levels and Confidence interval  
(e) Small sample and large sample. 

6. Hospital XYZ claims that the average days taken by their patients to recover from a particular disease is less than the average of all other hospitals, which is 60 days. A random sample of 100 patients, who are admitted in the XYZ hospital in the last year, gave the following recovery days distribution.

Recover

 

Test the Hospital claim at 5% level of significance. Comment their claim based on your investigation.
 
7. The mean daily sales of hand sanitizers in a medical shop was 50 pieces per store according to the previous year record. The Medical shop owner claimed that this year the sales increased due to the disease spread . Was the disease really increased the sales or not. Test the hypothesis with a 5% level of significance. The number of hand sanitizers sold in the past 12 days this year are 45, 65,70,42,55,65,72,86,25,42,45,30

 

Important Policies to be followed
1. Student Academic Integrity Policy*:

MEC upholds the spirit of academic integrity in all forms of academic work and any form of violation of academic integrity shall invite severe penalty. Any benefit obtained by indulging in the act of violation of academic integrity shall be cancelled.
All cases of violation of academic integrity on the part of the student shall fall under any of the below mentioned categories:
1. Plagiarism
2. Malpractice
3. Ghost Writing
4. Collusion
5. Other cases
If the student fails a module and has a proven case of academic integrity violation in this module, the student is required to re-register the module. This is applicable to first and second offenders of plagiarism.
 

1. Plagiarism
A. First offence of plagiarism
I. If a student is caught first time in an act of plagiarism during his/her course of study in any assignment other than project work, the student will be allowed to re-submit the assignment once, within a maximum period of one week. However, a penalty of deduction of 25% of the marks obtained for the resubmitted work will be imposed.
II. Period of re-submission: The student will have to re-submit the work one week from the date he or she is advised to re-submit.
III. If the re-submitted work is also found to be plagiarized, then that assessment will be awarded a zero mark. Re-submission of the work beyond the maximum period of one week will not be accepted and the assessment will be awarded a zero mark.

B. Second offence of plagiarism
If any student is caught second time in an act of plagiarism during his/her course of study (in a subsequent semester), the student will directly be awarded zero for the work in which plagiarism is detected. In such cases, the student will not be allowed to resubmit the work. A warning of suspension shall be issued, and student has to sign an undertaking and undergo counselling session in such cases.

2. Malpractice/Ghostwriting/Collusion
A. First offence of Malpractice/Ghostwriting/Collusion
If a student is caught in an act of Malpractice/Ghostwriting/Collusion for an assessment component irrespective of coursework or end semester, the student shall fail the module and shall be required to re-register the module
B. Second Offence of Malpractice/Ghostwriting/Collusion
If a student is caught a second time in an act of Malpractice/Ghostwriting/Collusion for an assessment component irrespective of coursework or end semester, the student shall fail the module. A warning of suspension shall be issued, and student has to sign an undertaking and undergo counselling session in such cases.

3. Third Offence of Academic Integrity Violation
If a student is caught a third time in an act of Academic Integrity Violation for an assessment component irrespective of coursework or end semester (in a subsequent semester), the student shall fail the module and also shall be suspended for one semester from the College, as recommended by institutional level academic committee, Chaired by the Associate Dean, Academic Affairs.

4. Fourth Offence of Academic Integrity Violation:
If a student is caught a fourth time in an act of Academic Integrity Violation for an assessment component irrespective of coursework or end semester (in a subsequent semester), the student shall fail the module and also shall be expelled from the College, as recommended by institutional level academic committee, Chaired by the Associate Dean, Academic Affairs.

5. Other cases
If a student commits an act of academic integrity violation as per the definition of “other cases” mentioned in the previous section or of a different nature, student’s case shall be forwarded to an institutional level academic committee, Chaired by the Associate Dean, Academic Affairs. The committee shall investigate the case by means of

a viva and/or a disciplinary hearing and shall take appropriate decision. The penalty that can be granted to a proven case of academic integrity violation which falls in this category of “other cases” can be a warning/component zero/ module fail/suspension/expulsion depending on the nature and gravity of the offence.

6. Types/Variations of Cases:
I. If plagiarism is detected in any component of one assessment, the deduction in marks will be applicable for the whole assessment, even if only the component or part submission alone needs to be resubmitted.

 

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  • Posted on : December 18th, 2018

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