# ENGG2851: Fernando Automotive is a World Famous Automobile Manufacturer in Brazil

Internal Code: 3EEJ **Question 1**

Fernando automotives is a world famous automobile manufacturer in Brazil. At present, it primarily produces cars and vans. It gets a profit of $5000 from each car and a profit of $18000 from each van. It has a limited supply of steel, plastic and paint, all of which are needed for manufacturing vehicles. It can get a maximum of 1,000,000 tons of steel, 1,200,000 tons of plastic and 800,000 kilolitres of paint each year.

Each car needs 1 ton of steel, 3 tons of plastic and 2 kilolitres of paint to be manufactured. However, each van needs, 5 tons of steel, 4 tons of plastic, and 2 kilolitres of paint. In addition, to maintain its credibility as a dominant player in both car and van manufacturing, the company needs to manufacture at least 100,000 cars and 100,000 vans each year. You, as the planning manager of the company, are asked to use linear programming techniques to determine how many cars and how many vans the company must produce each year to maximize profit.

- Assuming the number of cars manufactured each year is p and number of vans manufactured is q, write down all constraints as inequalities. Make sure to include the three manufacturing constraints, as well as the credibility constraints and the implied non-negativity constraints.
- Express the profit in terms of p and q.
- Use a graphical method to solve the optimization problem, and state how many cars and vans the company should manufacture each year for maximum profit, and what is the corresponding maximum profit. Show all workings.
- Now assume that in the following year, the demand for vans has fallen. Each van now only fetches a profit of $1000, and each car continues to fetch a profit of $5000. What is now the best solution in terms of number of cars and vans to maximize profit? Show all workings.
- Now, assuming that the profit levels stay at $1000 per van and $5000 per car, let us say the company decides to remove any credibility constraint and decides to manufacture the best combination of cars and vans for best profit. However, the supply constraints remain. What is now the optimal number of cars and vans manufactured for highest profit? Show all workings.
- If the company now decides to also manufacture motor bikes, a graphical method may not be best suited for finding the optimal solution. Explain why
this is the case and suggest an alternative method to solve the optimization problem.

**Question 2**

Fernando automotives has a main competitor, Excellent Motors (Hereafter EM). There are other car manufacturers besides these two in Brazil. In January 2015, both Fernando and EM plan to launch a new brand of car, and considering an advertising campaign to back it up. Currently, Fernando has a 35% market share, and EM has a 45% market share in Brazil. Both expect to increase this further.

They can advertise either on TV or via newspaper. Market research shows that TV advertisements are more effective when followed by another car advertisement, as this will re-enforce the idea that viewers need to buy a new car. On the other hand, newspaper advertisements are more effective when the competitors do not advertise in newspapers. Both companies do not know what advertising strategy the other company will adapt.

If Fernando and EM both advertise in TV, Fernando will get a 12% increase in market share, and EM will get a 8% increase. If both advertise in newspapers, they will both get a 4% increase. If Fernando advertises on newspaper while EM advertises on TV, Fernando will get a 10% increase while EM will lose 4% of the market. If EM advertises on newspaper while Fernando advertise on TV, EM will get a 3% increase while Fernando will lose 2% of the market.

- Assuming that each manufacturer has only two options (advertising in TV or advertising in newspaper), represent the scenario in a pay-off matrix. (3 marks)
- Is this a zero sum game? Justify your answer. (1 mark)
- What do you understand by a ‘dominant strategy’? Is there a dominant strategy for either player in this scenario? (4 marks)
- What do you understand by a ‘Pure strategy Nash Equilibrium’? Are there any Nash equilibrium states in the scenario mentioned above? (4 marks)
- Explain what you understand by a ‘mixed strategy Nash equilibrium’. (3 marks)
- Now assume that, new market research shows, when both companies advertise on TV, Fernando only gets a 7% increase in market share (rather than the 12%
- Furthermore, when Fernando advertises on TV and EM advertises on newspaper, Fernando in fact gets a 8% increase in market share (not the 2% loss as believed previously). Is there a pure strategy Nash equilibrium now? Come up with a mixed strategy for Fernando that will make it indifferent to the strategy chosen by EM. Similarly, can you devise a strategy for EM that will make it indifferent to the strategy adopted by Fernando? Is there a mixed strategy Nash equilibrium? Show all workings

**Question 3** **Part A)**

Fernando manufacturers are finding that the existing manufacturing plant is not sufficient for their manufacturing needs. Therefore, the management is contemplating either setting up a new plant, or upgrading the existing plant. Continuing without new or upgraded plants also, in theory, is an option. The company is intending that any capital investment will be ‘spread out’ and paid back within a period of ten years. The future of the company after ten years is uncertain and no plan could be made beyond ten years. Setting up a new plant would cost a capital investment of $ 100M (million), while upgrading the existing plant would cost $60M.

The PM team estimates that, if a new plant is set up, there is a 40% chance the annual profit will increase by $25M. There is a 30% chance that the profit increase will only be $15M annually, and 30% chance that the profit increase will only be $5M annually. If the plant is upgraded, there is a 80% chance that the annual profit will increase by $15M. There is a 10% chance that the profit increase will be $10M, and there is a 10% chance that the profit increase will only be $7M. If no upgrade is made, the company estimates there is a 60% chance that there will be no profit increase, There is a 20% chance that there will be a profit decrease of $5M, and there is a 20% chance that there will be a profit decrease of $10 M annually. The repayment for capital investments is not included in these profit predictions, and therefore will need to be deducted.

- Selecting the best investment option is often the first step in successful project management. State four investment option analysis techniques that you know of. Mention in each case whether they are qualitative or quantitative.

- Apply the ‘Expected Monetary Value’ (EMV) method in the above scenario to select the best investment option. Show all workings.
- The utility theory is sometimes used to select an investment option. Explain, using a simple example, why the utility analysis might be better than EMV analysis in certain scenarios.
- Apply the Expected Utility analysis in the above scenario to select the best investment option. Assume that f(x) = ?x is an appropriate utility function. Show all workings. What is the ‘certainty equivalent’ in each option?
- Comment on why the best option differs between the two analysis methods, and state with justification which one is more reliable in this context.

**Part B)**

Fernando manufacturers, in fact, decide to upgrade the existing factory, and they launch a project in partnership with a construction company to achieve this. The project is named ‘Project Reshine’ and will be implemented at a rapid phase, so as not to disrupt production. The project has five phases, as shown in Appendix A.

- Calculate the critical path of the project. Which activities are on the
critical path? ii. What is the maximum expected duration of the project in days?

**Appendix A** **Question 4**

Anil, Mehmet and Hien work in the chassis wiring department of Fernando ltd, which undertakes assembly line production. Chassis wiring is tedious and needs a lot of patience.

**Part A)**

To avoid boredom, Anil, Mehmet and Hien play a game: Once a car arrives for wiring, they measure the time until the next car arrives. If the next car arrives within 3 minutes, Mehmet and Hien pay $1 each to Anil. If the next car arrives within 3 to 5 minutes, Mehmet gets $1 each from Anil and Hien. If the next car arrives between 5 to 10 minutes, nobody pays or gains any money. If the next car arrives after 10 minutes, Hien gets $1 each from Anil and Mehmet. If on average, forty cars arrive for wiring within a shift of eight hours, what is the expected pay-off (or loss) for Anil, Mehmet and Hien respectively?

For this question you can assume that the probability of a random event occurring within T time units of the previous random event is given by p(t?T) = 1 – e-?T, where ? is the rate in which the random events are occurring. Show all steps.

**Part B)**

One day, only Anil is working in the chassis wiring department, as Mehmet and Hien are both on leave. Starting work at 8AM in the morning, he receives vehicles in the following order.

**Estimated time Vehicle Arrival time ****needed for wiring Vehicle Type ****V1 8.00 AM 10 mins Car ** **V2 8.01 AM 3 mins Van ** **V3 8.02 AM 7 mins Car ** **V4 8.03 AM 6 mins Van **

Anil can complete work in one of the following order: a) First come first served b) Shortest job first pre-emptive c) Fixed priority pre-emptive d) Round robin. Assume that any calculation takes negligible time for Anil and he would use a 2 minutes quantum if using round robin. Assume that in fixed priority scheduling, Cars have higher priority compared to vans.

- i) Calculate the average response time for each of the above mentioned scheduling methods.
- ii) Calculate the ‘throughput’ (inversion of average completion time) for each of the above mentioned scheduling methods.

iii) Comment on why the scheduling method which has the best average response is not the same as the method with the best throughput.

**Question 5**

The company Belstra pvt ltd is a mobile phone manufacturer, and launching a project to create a new model of mobile phone, Ringo Dingo . Refer to the following activity diagram of a project which has activities A, B, C, D, and E.

Which activities are on the critical path? (5 marks) ii. What is the maximum expected duration of the project in days?

iii. The Ringo Dingo prototype Steering Committee must decide whether

the option of using the Sustainable Product Lifecycle on the project is viable, given the associated risk. The estimated project cost is $80m and the additional cost of using the Sustainable Product Lifecycle is $20m, which would bring the total project cost to $100m. The expected revenue from the project based on the current market share is $200m but Belstra estimates that their market share could increase by as much as 20% as a result of marketing the product as “green technology”. This would increase the expected revenue for the project to $240m.

The probability of achieving the full 20% increase in market share and therefore reaching $240m in project revenue if the Sustainable Product Lifecycle is used is 80% with a 20% probability that only $200m in revenue will be achieved. If the Sustainable Product Lifecycle is not used, the probability of achieving $240m in revenue is only 25% with an 75% probability of still achieving $200m in revenue.

Calculate the Expected Monetary Value (EMV) for each option and recommend whether the Sustainable Product Lifecycle should be used.

Show all workings.

- Explain, using the understanding that you gained from this unit, and

using a suitable example, why Expected Monetary Value, Utility theory, and Game theory are all methods complementary to each other and can and must be used in specific contexts each.

**Question 6** **Part A**

Linear Programming is a mathematical model to achieve the best outcome (e.g. maximize profits, minimize costs), given some constraints.

a) Explain what you understand by an optimization problem. (2marks) b) Explain why the ‘simplex method’ is able to solve optimization problems that cannot be solved by the ‘graphical method’ of linear programming.

c) Consider the following scenario:

AgroBig Industries, an Australian company, has just purchased 10400 hectares of land in Panama, and plans to grow export crops on this piece of land. AgroBig senior management has decided they want to grow plantain, and tobacco, but unsure how many hectares should be devoted to each crop. They have the following information.

- Expected profit from a hectare of plantain (banana) is $ 50 thousand per year. Expected profit from tobacco is $42 thousand per year.
- The company plans to employ a work force of two hundred people. On average, they are each estimated to work two hundred days per year. A hectare of plantain needs 70 man-days per year of labour, whereas a hectare of tobacco needs only 2 man-days per year.
- A hectare of plantain needs 250 hours of irrigation per year, whereas a hectare of tobacco needs only 5 hours of irrigation. The total pump hours (irrigation hours) per year available in the facility are 125,000 hours.

Denoting the hectares of plantain as x

*1 *and the hectares of tobacco as x*2*, write down the three constraints as mathematical inequalities. ii. What is the expression for total profit per year y in terms of x1 and x*2*? iii. Write down five corner-point feasible solutions (CPF) to the problem. (State the values of x *1 *and x *2 *in each case). Show all workings. iv. Which is the best solution among these CPF solutions? What is the corresponding value of profit? Show all workings. **Part B**

Business environment is often conceptualized as a network (graph).

- a) State three reasons for modelling projects and business organizations as
networks (graphs). (

- b) A graph has 1475 nodes and 1726 links. What is the average degree of the graph? (You may use a calculator to compute the answer).

**Question 7**

Game theory is used in economics, social science and computer science to understand and predict the behaviour of people and intelligent entities.

a) Give two examples whereby a Nash equilibrium occurs in a contract management scenario

- b) Give two examples whereby two companies which are competitors in a market and engage in a classical game to promote their products may have a dominant strategy
- c) Consider the following normal game where Blue and Red can both play ‘C’ or ‘D’. The payoffs in each quarter are denoted in red and blue for the respective players. What are the Nash equilibrium states in this game? Is there a dominant strategy for either player? (3 marks)
- d) Oil producing countries need to maintain the price of oil from decreasing, and for this reason they need to limit the total production of oil. Therefore, they try to maximize their profile by predicting the production level of other countries. Consider the following hypothetical situation, where Saudi Arabia and Venezuela get varying profit margins for the oil they produce. Venezuela can either produce 1M barrels per day or 2M barrels per day, while Saudi Arabia can produce 4M barrels per day or 5M barrels per day. If the total production of the two countries is 5M barrels, then the profile margin is $16 per barrel. If the total production is 6M barrels, then the profile margin is $12 per barrel. If the total production is 7M barrels, then the profile margin is $8 per barrel.
- i) Illustrate this scenario in a pay-off matrix.
- ii) State if there are any Nash equilibrium states, and which are they?

iii) Is there a dominant strategy for either country?

**Question 8**

The Earned value method is commonly used to quantitatively measure how a project is tracking.

- a) In the case of a project which builds or produces a tangible object which has a market value (such as a house), explain why the ‘Earned value’ method cannot use present market value of the partially finished object to estimate the earned value of the project. Use suitable examples
- b) Explain why the BAC of the TCPI index must be re-assessed if the actual cost (AC) of the project has already exceeded the BAC. What will happen if the original BAC continues to be used? Use suitable examples in your explanation
- c) Give two examples of a scenario where a particular monotonous task in a project gets harder and harder as it is completed? Similarly, give two examples of a scenario where a particular monotonous task in a project gets easier and easier as it is completed?
- d) If a project at a particular time has less Earned Value than its Planned Value but more Earned value than the Actual Cost of the project, what does that mean? Conversely, if a project at a particular time has more Earned Value than its Planned Value but less Earned value than the Actual Cost of the project, what does that mean?
- e) Explain, with three suitable examples, how the EV method could be misleading in describing the health of the project at a given time

**Question 9**

Faraliers construction company is developing five separate sets of town houses in Pendle Hill. Each set is considered a project., and the five sets together are considered a program which share resources. The programme employs a specialist painter, who is good at creating luxury-looking interiors with cheap paint. The program also employs a scheduler. Staring on 21st August 2018 (which is considered day zero, with all subsequent days numbered 1,2,3,4 etc), the scheduler receives the following requests for the services of the specialist painter in the following days.

Assume that the specialist painter does not work over the weekend, and that the project numbers indicate their priority to Faraliers Ltd (the lowest number has the highest priority). The arrival days are business days (weekend not included).

The scheduler will use either a) FIFO order b) Shortest Job first pre-emptive c) Fixed priority but no pre-emption d) Round robin basis (with a three-day quantum) in his scheduling of tasks for the specialist painter.

- a) Based on the above, compute the average response time, in terms of business

**days, for each scheduling method. **

- b) Compute the average completion time, and throughput, in terms of business

**days, for each scheduling method.**

- c) Based on average response time, which is the best scheduling method? Based
on throughput, which is the best scheduling method? Comment on your findings.

**Question 10**

BanRay sunglasses have been experiencing a decline in sales, and to reboost sales they introduce discount system for their retailers who sell faster. A retailer making the next order within five days of the preceding order will receive a 30% discount. If the interval of orders is between five to ten days, the discount is 20%. If the interval is between ten to twenty days, the discount is 15%. If the interval is between twenty days and thirty days (a month), the discount is 10%. If the interval is between 30 days and 60 days, the discount is 5%. No discount is offered if the second order is more than 60 delayed.

Past experience tells that orders from a particular retailer arrives randomly, with an average frequency of two orders per month (you can assume a month consists of 30 days).

- Determine the probability that a customer receives
- Determine the average discount per arriving order.
- If a consignment of sunglasses costs $10,000 on average, and BanRay has 126 retailers, how much money should BanRay set aside each year to offset the discounts offered? For this question, assume that a month always consists of thirty days.
- Now assume that by next year, the sales of BanRay have picked up by 15% as a result if the reward scheme, but BanRay still has the same annual budget to offer discounts. Suggest, with justification, a revised reward scheme for retailers which fully uses the budget but does not exceed it. Show all workings.

**Question 11**

Redferni Pvt Ltd produces tables and chairs from wood and plastic. 12 kg of wood and 10 kg of plastic are needed to produce a table, whereas 5 kg of wood and 2 kg of plastic are needed to produce a chair. A table will fetch $300 in profit, where as a chair will fetch only $ 100. On a given month, a maximum of 12,000 kg of wood and 8000 kg of plastic will be available to the company. Since the company sells dining sets as well as individual chairs and tables, at least four chairs must be produced for every table produced.

- a) Use the simplex method to calculate how many tables and chairs must be

produced each month to maximize profit. Show all steps and workings.

- b) Now suppose that in the following month, a market survey is done which
indicates that the maximum demand for a table-and-for-chairs set in a month is 600 sets. Assume that nobody will buy a table by itself, and the company sells no other configuration of sets, but the company sells chairs by themselves. Explain how this new information will chance your calculations, and if necessary recalculate your answer according to this new constraint

- c) Explain why simplex method cannot be readily applied to minimisation
problems like it is applied to maximisation problems

**Question 12**

Data analytics can be applied in project management in different scenarios to make decisions.

(a) Describe three scenarios / examples where a Nash equilibrium may exist between two or more competing business entities. In each scenario, describe a catalyst event which will disturb this Nash equilibrium

(b) You have learned about the roles of leaders and managers, and the differences between them. Based on your understanding, discuss whether data analytics is more useful for leaders or managers. Give appropriate examples

- c) Describe two biologically inspired or nature-inspired algorithms and discuss how they can be used in data analytics
- d) Describe the difference between generic Hill-climbing and shotgun Hill-climbing algorithms
- e) Name and discuss two sectors of the industry where data analytics would be most applicable and have the most utility.

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