Franklin Tooling, Inc., manufactures specialty tooling for firms in the paper-making industry. All of their products are engineer-to-order and so the company never knows exactly what components to purchase for a tool until a customer places an order. However, the company believes that weekly demand for a few components is fairly stable. Component 135.AG is one such item. The last 26 weeks of historical use of component 135.AG is recorded below.

Use OM Explorer’s Time Series Forecasting Solver to evaluate the following forecasting methods. Start error measurement in the fifth week, so all methods are evaluated over the same time interval. Use the default settings for initial forecasts.

1. 3-Period Moving Average
2. 3-Period Weighted Moving Average forecast with weights of 0.7, 0.2, and 0.1
3. An Exponential Smoothing forecast using a starting forecast of 140 for week one and an α=0.25
4. Which forecasting method should management use, if the performance criterion it chooses is:
   1. MSE
   2. MAD
   3. MAPE

NZG is considering a compression installation project. The inlet compression project will reduce inlet pressure and allow extension of the plateau production rate while maximizing recovery from a natural gas field.

Once installed, the project will generate gross cash flows depending on the future natural gas price which in turn will be determined by the state of the world:

The project requires an initial outlay of $150,000.

A. What is the Sharpe ratio of the project? The current risk-free market interest rate is 5%.

B. NZG decided to securitize the project and auction it off. The winner of the auction will receive the project’s gross cash flow tabulated above in return for the bidding amount, which NZG will use to fund the project.

Ashley is an expected utility maximizer. His utility over his final wealth is given by and his initial wealth is $1,000,000. What is the maximum amount Ashley would be prepared to pay to win the auction? Assume that the auction is the only investment Ashley can make – i.e., if he does not win the auction, his wealth will stay at $1,000,000.

C. Another expected utility maximizer, Anthony, has a utility function over his final wealth given by  with an initial wealth of $1,000,000. If Ashley and Anthony know each other’s utility functions (as well as theirs), who will win the auction? Explain. (Hint: No calculation is necessary.)

Question 2
question 2.1
Give an example of a situation when an economy is in recession according to both definitions of recession and give another example of a situation when an economy may be in recession according to one of the definitions but not the other.

You answer.

question 2.2
Consider two identical countries. The only difference between them is that in country A the marginal propensity to consume (out of disposable income) MPC=0.4 and in country B MPC=0.7. The marginal tax rate t=0.2. I=20,000, G=10,000, NX=25,000-0.2Y (where Y is total income), c0=15,000.

a)   Calculate the multiplier in both countries (round up to two decimal places)

You answer.

b)   (i) What would be the equilibrium levels of output in country A and country B?

You answer.

(ii) Show the equilibrium levels of output in country A and country B on a well labelled graph with aggregate demand on the vertical axis and output (income) on the horizontal axis.

You answer.

c)   Now assume that consumers lose their confidence and decrease autonomous consumption c0 from 15,000 to 10,000. What will happen to output in both countries? Which country will have a larger effect on its GDP? Illustrate using the graph from part b).

You answer.

question 2.3
Usually investment depends on the interest rate. Briefly explain how an increase in the interest rate r would affect aggregate investment. Use a reference to the expected rate of profit in your explanation. (Word limit: max 100 words)

You answer.

Task (1)

You work as a material engineer at an aircraft development, manufacturing and maintenance company in the MENA region. Recently, the manufactured airplanes have been experiencing crashes after a couple of years in service. You have been assigned as a member in the investigation team to identify the main cause of the crashes.

1. The shape of the designed windows of the manufactured planes is square. The investigation team suggested that this design might be the main cause of the crashes. You must provide a possible explanation of the investigation conclusion from an engineering point of view.

2. Write the properties that should be considered when designing and manufacturing the coroners of the windows from an engineering point of view.

3. You have been given a sample of a malfunctioned airplane wing, which is made of aluminium. The company offered you an access to a tensile testing equipment and magnetic particles inspection equipment to investigate the malfunctioning behaviour. The results of your experiment were as follows:

Table 1: Tensile Testing Results (Load Extension)

1. Given that the length of the sample is 90 mm and the diameter of it is 7 mm.
   1. Draw the stress stain diagram.
   2. Find the yield stress (in KN/mm²).
   3. Find the ultimate tensile stress (in KN/mm²).
   4. At a point on the proportional section, calculate the modulus of Elasticity (Young’s modulus).

Hint: when calculating the Elasticity, use the stress strain numbers, not the force numbers

The managers of Tetron Medical Clinic are analyzing a proposed project. The following NPV distribution is given.

a. What is the project's expected NPV and standard deviation of NPV?

b. Compute CV?

c. What decision is appropriate for this project using NPV, standard deviation and CV?

Please show your work.

Write the R code

First, generate 1000 observations from a binomial distribution with n=30 and p=0.2 Use the 1000 observations you generated:

a) Generate poisson, binomial, negative binomial Diagnostic Distribution Plots using distplot.

b) Generate a histogram and overlay a kernel estimator of the density

(You can use: binom <- rbinom(n=1000,size=30, prob=0.2))

a) Explain why adjustment to beta such as Blume’s and Vasicek’s are necessary.

b) Assume betas for two stocks A and B are estimated to be 1.6 and 0.7 respectively. Calculate adjusted betas by using Blume’s method.

After 0.7 g of CoCl2⋅6H2O is heated, the residue has a mass of 0.321 g . Calculate the % H2O in the hydrate. What was the actual number of moles of water per formula unit CoCl2?