Consider an economy in which GDP is $8.4 trillion, public saving is -$0.2 trillion (yes, it is a negative number), taxes are $0.8 trillion, private saving is $3.0 trillion, export is $0.4 trillion, and import is $0.5 trillion. Calculate consumption, government purchases, national saving, and investment.

Consider a salient-role generator delivering power through a short transmission line to an infinite bus V∞=1∠0°, |Ea|=1.5. The active power delivered to the infinite bus is 0.7. We are given the generator reactances Xd=1.6 and Xq=1.0 and the line reactance XL=0.3. Neglect resistances, draw the phasor diagram and find Ea and Ia.

This is a work integrated assessment item. The tasks are similar to what would be carried out in the workplace.

Tully Tyres sells cheap imported tyres. The manager believes its profits are in decline. You have just been hired as an analyst by the manager of Tully Tyres to investigate the expected profit over the next 12 months based on current data.

•Monthly demand varies from 100 to 200 tyres – probabilities shown in the partial section of the spreadsheet below, but you have to insert formulas to ge the cumulative probability distribution which can be used in Excel with the VLOOKUP command.
•The average selling price per tyre follows a discrete uniform distribution ranging from $160 to $180 each. This means that it can take on equally likely integer values between $160 and $180 – more on this below.
•The average profit margin per tyre after covering variable costs follows a continuous uniform distribution between 20% and 30% of the selling price.
•Fixed costs per month are $2000.

(a)Using Excel set up a model to simulate the next 12 months to determine the expected average monthly profit for the year. You need to have loaded the Analysis Toolpak Add-In to your version of Excel. You must keep the data separate from the model. The model should show only formulas, no numbers whatsoever except for the month number.

You can use this partial template to guide you:

The first random number (RN 1) is to simulate monthly demands for tyres.
•The average selling price follows a discrete uniform distribution and can be determined by the function =RANDBETWEEN(160,180) in this case. But of course you will not enter (160,180) but the data cell references where they are recorded.
•The second random number (RN 2) is used to help simulate the profit margin.
•The average profit margin follows a continuous uniform distribution ranging between 20% and 30% and can be determined by the formula =0.2+(0.3-0.2)*the second random number (RN 2). Again you do not enter 0.2 and 0.3 but the data cell references where they are located. Note that if the random number is high, say 1, then 0.3-0.2 becomes 1 and when added to 0.2 it becomes 0.3. If the random number is low, say 0, then 0.3-0.2 becomes zero and the profit margin becomes 0.2.
•Add the 12 monthly profit figures and then find the average monthly profit.

Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show the grid (ie., row and column numbers) and be copied from Excel and pasted into Word. See Spreadsheet Advice in Interact Resources for guidance.

(b)Provide the average monthly profit to Ajax Tyres over the 12-month period.

(c)You present your findings to the manager of Ajax Tyres. He thinks that with market forces he can increase the average selling price by $40 (ie from $200 to $220) without losing sales. However he does suggest that the profit margin would then increase from 22% to 32%.

He has suggested that you examine the effect of these changes and report the results to him. Change the data accordingly in your model to make the changes and paste the output in your Word answer then write a report to the manager explaining your conclusions with respect to his suggestions. Also mention any reservations you might have about the change in selling prices.

The report must be dated, addressed to the Manager and signed off by you.

Monte Carlo Simulation

Tully Tyres sells cheap imported tyres. The manager believes its profits are in decline. You have just been hired as an analyst by the manager of Tully Tyres to investigate the expected profit over the next 12 months based on current data.

•Monthly demand varies from 100 to 200 tyres – probabilities shown in the partial section of the spreadsheet below, but you have to insert formulas to ge the cumulative probability distribution which can be used in Excel with the VLOOKUP command.
•The average selling price per tyre follows a discrete uniform distribution ranging from $160 to $180 each. This means that it can take on equally likely integer values between $160 and $180 – more on this below.
•The average profit margin per tyre after covering variable costs follows a continuous uniform distribution between 20% and 30% of the selling price.
•Fixed costs per month are $2000.

(a)Using Excel set up a model to simulate the next 12 months to determine the expected average monthly profit for the year. You need to have loaded the Analysis Toolpak Add-In to your version of Excel. You must keep the data separate from the model. The model should show only formulas, no numbers whatsoever except for the month number.

You can use this partial template to guide you:

The first random number (RN 1) is to simulate monthly demands for tyres.
•The average selling price follows a discrete uniform distribution and can be determined by the function =RANDBETWEEN(160,180) in this case. But of course you will not enter (160,180) but the data cell references where they are recorded.
•The second random number (RN 2) is used to help simulate the profit margin.
•The average profit margin follows a continuous uniform distribution ranging between 20% and 30% and can be determined by the formula =0.2+(0.3-0.2)*the second random number (RN 2). Again you do not enter 0.2 and 0.3 but the data cell references where they are located. Note that if the random number is high, say 1, then 0.3-0.2 becomes 1 and when added to 0.2 it becomes 0.3. If the random number is low, say 0, then 0.3-0.2 becomes zero and the profit margin becomes 0.2.
•Add the 12 monthly profit figures and then find the average monthly profit.

Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show the grid (ie., row and column numbers) and be copied from Excel and pasted into Word. See Spreadsheet Advice in Interact Resources for guidance.

(b)Provide the average monthly profit to Tully Tyres over the 12-month period.

(c)You present your findings to the manager of Ajax Tyres. He thinks that with market forces he can increase the average selling price by $40 (ie from $200 to $220) without losing sales. However he does suggest that the profit margin would then increase from 22% to 32%.

He has suggested that you examine the effect of these changes and report the results to him. Change the data accordingly in your model to make the changes and paste the output in your Word answer then write a report to the manager explaining your conclusions with respect to his suggestions. Also mention any reservations you might have about the change in selling prices.

The report must be dated, addressed to the Manager and signed off by you.
(Word limit: No more than 150 words)

I actually did question 1-7, but I do have some problems in 8 and 9.

part I: Project Rescue (25 points) The Park Rangers protecting our national forests typically carry communication and sighting equipment that is used to help locate lost hikers, forest fires, airplanes crashes and other such like. In one instance, a light plane P crashed in a dense part of the forest, with the crash occurring to the northeast of a ranger R who witnessed the event. The witness was located 12 miles due east of the ranger station S. The bearing from the witness to the crash site was 20º, while the bearing from the Ranger Station, based on the smoke plume from the wreckage, was 52º. Answer the questions that follow, showing work to support your answers and rounding answers to nearest tenth, unless otherwise indicated. Answer the “Why?” questions in complete sentences.   

1) Use the information given to draw RSP. Draw the triangle large enough to fit the box below, labeling all given information and measurements appropriately.

2) What is the measure of ∠ PSR? Why?


3) What is the measure of ∠ PRS?



4) What is the measure of ∠ RPS? Why

5) Can we use the Law of Sines to find the distances SP and RP? Why/why not?

6) What is the distance SP from the ranger station to the crash site?

7) What is the distance RP from the ranger who witnessed the crash to the crash site?

part II: Project Rescue (15 points) Redraw the figure in Part I in the box below. A search and rescue team T is assembling at a point that is 7 miles due east of the ranger station S, directly between the ranger station and the witness. Draw a line connecting point T and point P.

8) How far is the rescue team T from the crash site?
9) What direction should they head to reach the crash site? Answer in terms of a bearing.

Problem Scenario: Following is a problem description. For all hypothesis tests, you MUST state the statistical test you are using and use the P-VALUE METHOD through Microsoft Excel to make your decision. Show all steps, calculations, and work. For confidence intervals there is a specific Excel tool for each interval.  Treat each part of the question as a separate problem -- we use the same data set but are answering different “research questions”.

Many parts of cars are mechanically tested to be certain that they do not fail prematurely. In an experiment to determine which one of two types of metal alloy produces superior door hinges, 40 of each type were tested until they failed. To evaluate how long hinges made with the different alloys would last, the number of openings and closings was observed and recorded (to the closest 0.1 million). Car manufacturers consider any hinge that does not survive 1 million openings and closings to be a failure., A statistician has determined that the number of openings and closings is normally distributed.

NOTE: use ONLY the P-value method for hypothesis tests.

Number of Openings and Closings

a.) Estimate with 90% confidence the difference in the number of openings and closings between hinges made with Alloy1 and hinges made with Alloy 2. Interpret the interval.

b.) The quality control manager is not only concerned about the openings and closings of the hinges but is also concerned about the proportion of hinges that fail. Can we infer at the 10% significance level that the proportion of hinges made with Alloy 2 that fail exceeds 18%?

Two chemical factories are discharging toxic waste into a large lake, and the pollution level at a point ? miles from factory A toward factory B is ?(?) = 3?2 − 72? + 576 parts per million for 0 ≤ ? ≤ 50. Find where the pollution is the least

(a) Can income share of the capitalist class decline when wealth-income ratio is increasing? Explain. (b) According to Miles Corak (from the Marc Sumerlin lecture series), what should not be the focus of a policy-maker to increase intergenerational mobility? Explain.

A train accelerates at 1.41 m/s² from rest to a steady speed in 68.48seconds. It maintains that speed for 29.55 miles and then starts slowing down at 1.39 m/s² until coming to a stop at its destination. What is the total distance traveled in meters?