Quantitative Methods Assignment

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Hi, I need a detailed answer for Question 1 only.

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BUS107e Quantitative Methods Group-based Assignment July 2017 Presentation BUS107e Group-based Assignment GROUP-BASED ASSIGNMENT This assignment is worth 30% of the final mark for BUS107e Quantitative Methods. The cut-off date for this assignment is 18 October 2017, 2355hrs. This is a group-based assignment. You should form a group of 4 members from your seminar group. Each group is required to upload a single report to Canvas via your respective seminar group. Please elect a group leader. The responsibility of the group leader is to upload the report on behalf of the group. It is important for each group member to contribute substantially to the final submitted work. All group members are equally responsible for the entire submitted assignment. If you feel that the work distribution is inequitable to either yourself or your group mates, please highlight this to your instructor as soon as possible. Your instructor will then investigate and decide on any action that needs to be taken. It is not necessary for all group members to be awarded the same mark. SINGAPORE UNIVERSITY OF SOCIAL SCIENCES (SUSS) Page 2 of 7 BUS107e Group-based Assignment Important Note: Grading of GBA Submissions Marks awarded to your assignment are based on the following guidelines: 1. 80% of the marks are allocated to the content of your answers:  The marks awarded to what your answers cover depend on the extent to which they cover the key points that correctly and comprehensively address each question.  The key points should be supported by evidence drawn from course materials and, wherever relevant, from other credible sources. 2. 20% of the marks are allocated to the presentation of your answers: Wherever applicable, the marks awarded to how your answers are presented depend on the extent to which your answers:  form a sound reasoning by developing those key points in a clear, logical and succinct manner;  provide proper and adequate in-text citations and referencing to content drawn from course materials and other credible sources;  strictly follow APA formatting and style guidelines1, in particular for:  in-text citations and end-of-report references;  the identification of figures and tables;  use, wherever relevant, the specialised vocabulary and terminology commonly used in discussions about the topic(s) covered by each question;  provide a reference or bibliography at the end of the main report;  include the less relevant details in an Appendix;  use sentence constructions that are grammatically and syntactically correct;  are free from spelling mistakes; present the workings, numerical formulations and results in a logical manner that follows the APA formatting and style guidelines;  design and present graphs, diagrams and plots that follow the APA formatting and style guidelines;  are highly original;  have proper formatting, which may:  include a properly formatted cover page;  respect the answer length/word count set out in the assignment guidelines, if any is prescribed;  present answers in paragraphs with proper spacing and page margins;  include page numbers and appendices, if necessary. 1 You can find a short tutorial on the APA formatting and style guidelines here: https://is.gd/mgEOnC . Additional details (pertaining to tables and figures) can be found here: https://is.gd/O4vDdT . SINGAPORE UNIVERSITY OF SOCIAL SCIENCES (SUSS) Page 3 of 7 BUS107e Group-based Assignment The following statements apply to all questions: Develop the essential knowledge and interpersonal skills to work effectively in a team. You are supposed to work on all questions as a team. Do not spilt the assignment among your group members in a way that “member 1 is doing question 1, member 2 is doing question 2, etc.” Question 1 Jake is the regional head of Modern Automobile Inc. Jake is responsible for selling and manufacturing vehicles for the region. Jake has two products in his product portfolio: one model of SUV (SUV) and one model of family sedan (Car). The plans for production and sales are prepared in the quarterly basis. Although Jake has a considerable amount of autonomy on how to run his business in the region, Modern Automobile Inc. places a guideline on the maximum number of vehicles can be produced in each quarter. The maximum numbers of SUV and Car allowed for Jake to manufacture for each quarter are given below: Maximum Allowed 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter SUV in units 200 300 100 400 Car in units 400 900 700 1000 The production of one unit of SUV consumes 1.8 ton of steel, where as one unit production of Car consumes 0.8 ton of steel. Due to the lack of steel mills in the region, Jake only manages to obtain 1000 ton of steel supply for each quarter. Since last year, the regional government has imposed an environmental regulation on fuel efficiency. The fuel efficiency is measured by mile-per-gallon (mpg). The average mpg for all vehicles Jake manufactures this year must be at least 40 mpg. Petrol guzzling SUV only achieves 20 mpg, whereas more fuel efficient Car can deliver 45 mpg. When a vehicle is produced, it is either directly sent to dealers or kept at factory parking lot for later delivery (to dealers). The general accounting practice for Jake is that any vehicle still at the factory parking lot at the end of each quarter incurs an inventory holding cost. Inventory holding costs are $200 per unit per quarter for SUV and $100 per unit per quarter for Car. Since Jake’s background is in production management, he understands very well that certain costs occur if production volume increases (partly due to over worn production facility) or decreases (partly due to cost related to idling capacity) from a quarter to the next. One unit increase in the production volume of SUV from one quarter to the next incurs $100, whereas one unit increase in the production volume of Car from one quarter to the next incurs $50. On the other hand, one unit decrease in the production volume of SUV from one quarter to the next incurs $80, whereas one unit decrease in the production volume of Car from one quarter to the next incurs $30. It is not a secret to anybody that SUV is a lot more profitable product than Car. Excluding the inventory holding cost and costs related to the increase or decrease in production volume, each unit of SUV contributes $2000 to the profit, whereas each unit of Car only contributes $150 to the profit. SINGAPORE UNIVERSITY OF SOCIAL SCIENCES (SUSS) Page 4 of 7 BUS107e Group-based Assignment (a) Describe the decision making problem for Jake. Apply linear programming model to develop a formulation for the decision making problem of Jake. (20 marks) (b) Use Microsoft Excel to solve the formulation in Question 1(a). Your answer must include the sensitivity report. (5 marks) (c) Imagine you are working for Jake. Interpret the sensitivity report you obtained in Question 1(b) and prepare an analysis report for Jake in 500 words. Your analysis report may include subjects like, for example, whether it would be beneficial for the company if they try to persuade the regional government to relax the mpg requirement or what would be the impact on the production plan if profit contribution of SUV falls in future. (15 marks) Question 2 Jerome is working for a holiday camp located in a remote island. Jerome is responsible for arranging ferry services for camp visitors. It has been a long established practice that the contracts with the ferry service providers are signed on 28th December for the coming year. It is 26th December. While others are recovering from Christmas Party they had last night, Jerome is busy to forecast the number of visitors to his holiday camp next year. Naturally, the more the visitors, the more ferry services are needed. Data on the number of visitors are collected quarterly since the contract period with the ferry service providers is quarterly. The following table shows the number of visitors in past 8 years: Year 8 years ago 7 years ago 6 years ago Quarter Visitors Year Quarter Visitors 1 45 4 years ago 1 64 2 138 2 190 3 112 3 140 4 76 4 108 1 46 3 years ago 1 81 2 128 2 224 3 121 3 202 4 75 4 133 1 50 1 110 2 years ago 2 138 2 327 3 112 3 261 4 77 4 154 SINGAPORE UNIVERSITY OF SOCIAL SCIENCES (SUSS) Page 5 of 7 BUS107e Group-based Assignment 5 years ago 1 2 3 4 50 147 130 77 Last year 1 2 3 4 130 354 305 223 (a) Imagine you are working for Jake. Jake needs to have the forecast on the number of visitors for each quarter this year. Employ the techniques of time series modelling to discuss what method should be used. Your discussion should include how you are going to use the forecast method in forecasting the visitor numbers. You may include a graph or chart on the number of visitors of past 8 years to justify your discussion. (10 marks) (b) Use the method you choose in Question 2(a) to forecast the number of visitors in each quarter of this year. (20 marks) Question 3 Jamie is the head of product development team at Three Stars Electronics (TSE). Currently, Jamie is evaluating two product development projects. Those two potential products are code named as Product A and Product B. Product A will be designed for the US market. If Jamie chooses Product A project, Jamie has to decide whether it will be developed as high end product or low end product. The size of profit TSE will get from Product A depends on the performance of American economy. The best guess at the moment is that there are 60% chance that American economy will be good by the time Product A will be on the market. However, there are 40% chance that American economy will do poorly when the Product A will hit the market. If American economy is doing good, low end designed Product A will deliver USD15 million profit to TSE. If American economy is doing poorly, low end designed Product A will deliver the profit of USD10 million. However, there is a little bit tricky part for the development of the high end designed Product A. High end designed Product A will require a specific component called Alpha. The problem is Alpha is still under development stage and early test results indicate that the component may catch fire under certain circumstances. Jamie needs Alpha to be ready in two-month time to complete the development of high end Product A. When Jamie asked their honest opinion on the chance of Alpha being ready in two months, the head of research department replied, “It is 50-50, Jamie. That is my fair judgement.” If Alpha is not ready, the high end designed Product A should be shipped with component Beta which is already available from the older generations of products. However, high end designed Product A with component Beta will be seen as a joke. Even American economy is doing well when Product A hits the market, it will result in a loss of USD10 million. If American economy is doing poorly when Product A hits the market, it will result the loss of USD40 million. Nevertheless, abandoning the development of Product A is not an option since Jamie will be personally responsible for the write-off of the development expenses of USD100 million. SINGAPORE UNIVERSITY OF SOCIAL SCIENCES (SUSS) Page 6 of 7 BUS107e Group-based Assignment However, if the development of Alpha is completed within time, high end designed Product A with the component Alpha will deliver the profit of USD 40 million if US economy is doing well. Even American economy is doing poorly, high end designed Product A will still deliver the profit of USD15 million. Product B will be designed for Japanese market. Product B can also be designed for high end product or low end product. If Product B is designed for high end product, it will require a special component called Jetta. Jetta is shipped from a sole supplier in Japan. Unfortunately, the diplomatic relationship between TSE’s country and Japan has been very shaky in recent months. There are about 20% chance that Japanese government blocks the shipment of Jetta to TSE by the time that the development project of Product B needs the component. If Jetta is not available, Product B has to be designed as a low end product. The low end designed Product B will return the profit of USD12 million to TSE if Japanese economy is strong when Product B is introduced to the market. If Japanese economy is weak, low end designed Product B will return the profit of USD8 million. Even if Jetta is available, it is still up to Jamie whether to develop Product B as a high end product or a low end product. If Japanese economy is doing good, high end designed Product B will return the profit of USD20 million. On the other hand, high end products do not sell well in Japan when economy is poor. If Japanese economy turns out to be weak when Product B hits the market, high end designed Product B will only deliver the profit of USD1 million. At the moment, the outlook for Japanese economy is not as good as American’s. There are 70% chance that Japanese economy will be weak when Product B will be introduced to the market. There are only 30% chance that Japanese economy will be strong. Jamie is going to meet his boss in two hours. Given the available resources to Jamie, he can commit to only one product development project. It is time for Jamie to make a decision. Discuss which option Jamie should choose. Develop a Decision Tree to justify your answer. (30 marks) ---- END OF ASSIGNMENT ---- SINGAPORE UNIVERSITY OF SOCIAL SCIENCES (SUSS) Page 7 of 7 ...
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Tutor Answer

charlisewrite
School: University of Maryland

there you go buddy

Running head: QUANTITATIVE METHODS`

Sensitivity Analysis

Student Name:

Institution:

1

QUANTITATIVE METHODS

2

`
Introduction

This is a maximization linear programming problem. Therefore formulation of
equations is quite important step to solving the problem. The maximum numbers of SUV and
Car allowed for Jake to manufacture for each quarter are given below:
Maximum Allowed

SUV in units

Car in units

1st Quarter

200

400

2nd Quarter

300

900

3rd Quarter

100

700

4th Quarter

400

1000

Formulation of Linear Equations
Since this is a profit maximization problem, we form decision variables as follow;
Decision variables
Let X= number of SUV manufactured in a quarter
Y = the number of Cars manufactured in a quarter.
Next is the formulation of objective function based on the profit per the type of car
manufactured;
Maximize: 2000X + 150
Subject to constraints:
1.8X +0.8 Y ≤ 1000 (Num...

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