A company manufacture two different products A and B, each unit of product A costs 8 OR and each unit of product B costs 4 OR. The company insists that total costs for the two products be 500 OR. Assuming that company manufactures in total 85 products. How many product are of type A? (solve the problem using matrices applications)

MTM (MASC 10004) – Spring – 2020 – CW (Assignment) – QP MEC_AMO_TEM_034_01 Page 1 of 8 Instructions to Student  Answer all questions.  Deadline of submission: 04/06/2020 23:59  The marks received on the assignment will be scaled down to the actual weightage of the assignment which is 50 marks  Formative feedback on the complete assignment draft will be provided if the draft is submitted at least 10 days before the final submission date.  Feedback after final evaluation will be provided by 18/06/2020 Module Learning Outcomes The following LOs are achieved by the student by completing the assignment successfully 1) Apply appropriate techniques of algebraic operations to management applications. 2) Carry out the operations on matrices and apply them to solve simple application problems. 3) a. Construct a linear cost, revenue and profit functions and conduct breakeven analysis Assignment Objective 1. To test understanding of students on main Mathematical concepts lie under the above Los. 2. Test the ability of the students to apply Mathematical concepts in business problems. Assignment Tasks 1. Zid, Salim and Hamad purchased soft drinks of 5 different brands A,B, C, D and E each person purchased from each brand as following quantity matrix 𝑸 show: 𝐴 𝐵 𝐶 𝐷 𝐸 𝑍𝑖𝑑 15 2 5 9 5 𝑆𝑎𝑙𝑖𝑚 10 4 7 2 12 𝐻𝑎𝑚𝑎𝑑 9 6 12 8 11 If the brands costs are given by the matric 𝑪 IN SEMESTER INDIVIDUAL ASSIGNMENT Module Code: MASC 10004 Module Name: Mathematical Technique for Managers Level: 1 Max. Marks: 100 MTM (MASC 10004) – Spring – 2020 – CW (Assignment) – QP MEC_AMO_TEM_034_01 Page 2 of 8 𝑪 = [ 0.6 1 0.2 1.5 0.8] Find the amount of money spend by each person if it is given by multiplying the quantity by the costs of the brands, and conclude who spend more (6 marks) 2. A company manufacture two different products A and B, each unit of product A costs 8 OR and each unit of product B costs 4 OR. The company insists that total costs for the two products be 500 OR. Assuming that company manufactures in total 85 products. How many product are of type A? (solve the problem using matrices applications) (12 marks) 3. Find the matrices x and y if 2𝑥 − 2𝑦 = [ 6 −4 −2 4 −14 10] 𝑎𝑛𝑑 𝑥 + 𝑦 = [ 4 2 5 −2 −1 −7 ] (11 marks) 4. Let 𝐶 = [ −1 0 3 2 3 1 −2 2 2 −4 ] and 𝑀 = [ −3 1 −1 0 1 3 7 −6 2 ]. Find: det(|𝐶|𝑀𝑇 ), evaluate |𝐶| from 2nd row (13 marks) 5. A college conference has total 160 papers, with 25 papers more from mathematics department than doubled the papers from statistic department. Find the number of statistics papers in the college conference. (8 marks) 6. Given the equation: [ 5 − 𝑡 2 −1 −3 ] + 2 [ 4𝑦 5 2 10𝑥 + 11 6 ] = [ 𝑥 −5 0 6 ] − 3 [ 6 −4 −1 −𝑡 ] Find x,y and t (13 marks) MTM (MASC 10004) – Spring – 2020 – CW (Assignment) – QP MEC_AMO_TEM_034_01 Page 3 of 8 7. A firm that make pens plan to make 1000 pens a week, Based off their production cost through the years, they figure that it will cost them 100 Baisa to make each pen. There will be also a cost of running the equipment for a week that they figure to be 35 Rials for the whole week, regardless of how many pens they make. The factory decides to sell its 1000 pens for 200 Baisa each. a. Find the weekly profit function then find the profit of selling all 600 pens.(6 marks) b. How many weeks the firm need in order to break even (8 marks) 8. a. Suppose the cost to produce some commodity is a linear function of output. Find cost as a function of output if costs are 5,000 Rials for 550 units and 8,000 Rials for 860 units. (4 marks) b. Find the output if the cost is decrease to 10000 Rials. (2 marks) c. Find the cost of produce the commodity if there is no output (2 marks) 9. Given a matrices 𝐴 = [ 3 6 −2 −4 ], 𝐵 = [ 1 −2 1 4 ], 𝐶 = [ 12 12 −4 −2 ], a. Find a matrix 𝑋 if : 2𝐴 + 𝑋𝐵 = 𝐶 (13 marks) b. Prove that matrix A is singular matrix (2 marks) Rules & Regulations:  Title Page must have Assignment Name, Module name, Session, your name, ID, and the name of the faculty.  Softcopy in word format is to be submitted through Turnitin link on Moodle. Guidelines:  Assignment must be computer typed.  Font – Size – 12  Question number and subparts should be written clearly in Font Size 14, Bold, Capital and Underline.  Each student has to do the assignment individually.  The units of the final results should mention MTM (MASC 10004) – Spring – 2020 – CW (Assignment) – QP MEC_AMO_TEM_034_01 Page 4 of 8 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 MTM (MASC 10004) – Spring – 2020 – CW (Assignment) – QP MEC_AMO_TEM_034_01 Page 5 of 8 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. II. If plagiarism is detected in a group assessment, all students of the group will be considered as having committed an act of plagiarism and the policy will then be applied to all students III. If plagiarism is detected in any component of a group 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. MTM (MASC 10004) – Spring – 2020 – CW (Assignment) – QP MEC_AMO_TEM_034_01 Page 6 of 8 All students of the group would be considered as having committed an act of plagiarism and the policy will then be applied to all the students of the group. IV. If the assessment consists of components or part submissions that could be a group assessment component (e.g. group assignment) and an individual assessment component (e.g. individual reflection), the following will be applicable: a. If plagiarism is detected in the group assessment component, all students of the group will be considered as having committed an act of plagiarism, The policy will then be applied to all students of the group. Group assessment component will be resubmitted as per the policy. b. If plagiarism is detected in the individual assessment component, the individual assessment component will be resubmitted and the policy will then be applied to that student alone. c. For both (a) and/or (b), the deduction in marks will be applicable for the whole assessment. * for further details Refer to MEC Student Academic Integrity Policy in Student Handbook. 2. Late Submission Regulations: It is the students’ responsibility to check all relevant timelines related to assessments. As per the Assessment Policy at MEC, late submissions are allowed for one week (5 working days) for all UG modules with a penalty. In such cases, a deduction of 5% of the marks obtained for the submitted work shall be imposed for each working day following the last date of submission till the date of actual submission. Assessment documents submitted beyond a period of one week (5 working days) after the last date of submission will not be accepted and will be awarded a zero for that assessment. In cases where the submission has been delayed due to extenuating circumstances, the student may be permitted to submit the work without imposing the late submission policy stated above. The extended period of submission will be one week from the original last date of submission. In such cases, the student is expected to submit the supporting certificates on or before the original last date of submission of the assessment and the decision of extension rests with faculty responsible for the assessment .The late submission policy shall be applied if the student fails to submit the work within one week of the original last date of submission. Students may contact their teachers for clarification on specific details of the submission time if required. 3. Research Ethics and Biosafety Policy To protect and respect the rights, dignity, health, safety, and privacy of research subjects involved including the welfare of animals and the integrity of environment, all student projects are expected to be undertaken as per the MEC Research Ethics and Biosafety Policy. Accordingly the following shall apply. MTM (MASC 10004) – Spring – 2020 – CW (Assignment) – QP MEC_AMO_TEM_034_01 Page 7 of 8  Research and other enterprise activities shall be conducted by maintaining the high ethical standards consistent with national and international standards and conventions.  Any research at MEC that is categorized as high-risk research shall be subject to review and approval by the Research Ethics and Biosafety Committee.  Research activities involving collection of human or animal tissues and manipulation of microbial, animal or plant cells shall be subject to review and approval by the Research Ethics and Biosafety Committee.  Participants involved in research must be informed about the purpose of research and intended uses of research findings. Written consent must be obtained from people involved prior to the commencement of research.  Data obtained from participants must be treated with high confidence and should be used only for the intended purpose of research. Assessment Evaluation Criteria Classification And % Range Reflection and critical analysis. Knowledge and Understanding/ Application of Theory Evidence of Reading Referencing and Bibliography Presentation, Grammar and Spelling Outstanding Highly competent analytical skills and reflective practice, demonstrating personal learning and growth, insight into required professional values and principles and professional development planning. Extensive knowledge and depth of understanding of principles and concepts and /or outstanding application of theory in practice. Evidence of reading an extensive range of educational literature/research and where applicable workplace strategies, policies and procedures. Accurate referencing and bibliography correctly using appropriate referencing style Excellent presentation, logically structured, using correct grammar and spelling, excellent crossreferencing and links to supporting evidence Excellent Strong analytical skills and reflective practice used, demonstrating personal learning and growth, insight into required professional values, principles and competencies and professional development planning. Excellent knowledge and understanding of principles and concepts and /or excellent knowledge and understanding of the application of theory in practice Evidence of reading a wide range of educational literature/research and where applicable, workplace strategies, policies and procedures. Appropriate referencing and bibliography correctly using appropriate referencing style Good presentation, competently structured, using correct grammar and spelling, clear and easy to use links to supporting evidence Very Good Quality Good use of analytical skills and reflective practice demonstrating personal learning and growth, insight into required professional values, principles and competencies and professional development planning. Good knowledge or key principles and concepts and/or good knowledge of the application of theory in practice Evidence of reading a good range of educational literature/research and where applicable workplace strategies, policies and procedures. Generally well referenced with correct use of the appropriate referencing style Reasonable presentation, completely structured, acceptable grammar and spelling, acceptable links to supporting evidence Good (Acceptable) Acceptable use of analytical skills and reflective practice demonstrating personal learning and growth, insight into required professional values, principles and competencies and professional development planning. Acceptable knowledge of key principles and concepts and/or knowledge of the application of theory in practice Evidence of reading an appropriate range of educational literature/research and where applicable, relevant workplace policies and procedures Adequate referencing. Generally accurate use of appropriate referencing style Adequate presentation and structure, acceptable grammar and spelling, adequate links to supporting evidence Adequate/ Satisfactory Adequate use of analytical skills and reflective practice demonstrating personal learning and growth, insight into required Adequate knowledge of key principles and concepts and/or satisfactory evidence of the application of theory in practice. Evidence of minimal reading of educational literature/research and where applicable relevant Adequate referencing. Appropriate referencing style used but may contain some inaccuracies. Weak presentation , satisfactory structure, grammar and spelling, links to supporting evidence MTM (MASC 10004) – Spring – 2020 – CW (Assignment) – QP MEC_AMO_TEM_034_01 Page 8 of 8 professional values, principles and competencies and professional development planning. workplace policies and procedures Weak /Poor (all learning outcomes not adequately met) Little use of analytical skills and reflective practice demonstrating personal learning and growth, insight into required competencies and/or professional development planning. Professional values and principles not reflected in the submission. and/or Insufficient/no use of analytical skills and reflective practice demonstrating personal learning and growth, insight into required competencies and professional development planning Little evidence of knowledge of key principles or concepts and/or little evidence of the application of theory in practice and/or No evidence of knowledge of key principles or concepts and/or no evidence of application of theory in practice Little or no evidence of reading outside of the course textbook and/or reference to relevant work place policies and procedures and/or No evidence of reading outside of the course textbook and/or reference to relevant workplace policies and procedures Little or no referencing, incorrect style, or very inaccurate use of appropriate referencing style Poor presentation, grammar and spelling, links to supporting evidence and/or Unacceptable presentation, grammar and spelling, structure is very poor, links to supporting evidence