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The year is 2120, and Eltron Musk is an adventuresome entrepreneur. Mr. Musks company, EM, Inc. (EMI), maintains an Earth-global and an interplanetary presence. EMI is a for-profit company and aims to make the most of its profits. Additionally, EMI aims to keep its costs as low as possible. EMI has hired you, as a consultant, to assist the company with a few of its projects. Consequently, you must analyze the following problems/projects and create solutions for EMIs executives.

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Project #1: New Propulsion Technology

EMI discovered a new technology to adapt its rocket technology to undersea usage for possible military operations. However, management is also interested in another possible application of the new technology for extra-dimensional travel. Thus, if the Total Quarterly Sales Projection (TQSP) for year #5 (i.e., the forecast for year #5) exceeds $17.5 billion, then EMI desires to use the technology for both undersea and extra-dimensional propulsion. If the TQSP for year #5 is less than $17.5 billion but more than $17.4 billion, then EMI will refrain from attempting the extra-dimensional application of the technology. If the year #5 TQSP is less than or equal to $17.4 billion, then EMI will completely refrain from the new technology. Note: the year #5 forecast is a sum of the values for all four quarters.

Using regression, create the year #5 sales projection by concurrently examining seasonality and trend in Table 1.0. Report the recommended course of action to EMI based upon a 1-year forecast (i.e., a forecast for year #5). How far should EMI take the new technology? Justify your answer. Present key data. Provide a compelling argument for your recommendation. Include (but do not limit your answer to) the following in your report:

1. What are the projected quarterly forecast values for year 5?
2. What is the forecasts MSE?
3. What is the forecasts MAE?
4. What is the forecasts MAPE?
5. Are your forecast accuracy measures meaningful? Why or why not?

Clearly identify your answers.

Table 1.0

Year	Quarter	Sales (In Billions)
1	1	4.33
	2	4.42
	3	4.23
	4	4.54
2	1	4.34
	2	4.55
	3	4.45
	4	4.56
3	1	4.56
	2	4.00
	3	4.12
	4	4.53
4	1	4.35
	2	4.56
	3	3.09
	4	4.01

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Project #2: TIN

EMI maintains a system known as The Interplanetary Network (TIN), which ships space-station items (measured in units) between the planets. EMI is concerned that TIN is cost-inefficient. Quarterly, EMI ships components from Earth, Mars, Saturn, and Neptune to Mercury, Venus, Jupiter, and Uranus.

The following table (Table 2.0) contains information from NASAs Jet Propulsion Lab, regarding the distance of the planets from the Sun.

Table 2.0

Planet	Distance from Sun in Millions of Miles
Mercury	37.2
Venus	65.1
Earth	93
Mars	139.5
Jupiter	483.6
Saturn	892.8
Uranus	1785.6
Neptune	2790

The following table (i.e., Table 3.0) contains quarterly costs (in thousands) per unit to ship from one planet to the next:

Table 3.0

	Mercury	Venus	Jupiter	Uranus
Earth	323	132	298	321
Mars	233	321	229	301
Saturn	121	311	392	309
Neptune	322	209	232	299

The following are quarterly planetary demands: Mercury 999 units, Venus 973 units, Jupiter 1151 units. Uranus 1230 units.

Quarterly, Earth can supply 1074 units, Mars can ship 1084 units, Saturn can ship 1133 units, and Neptune can ship 1062 units.

Presently, EMI quarterly costs for the network exceed $1 billion.

Create a report for EMI executives. Your report must address (but is not limited to) the following:

1. Is EMI losing money in its current shipping costs?
2. What is the linear-programming solution to this problem? Report your linear program.
3. How should EMI ship through the network?
4. What is the cheapest overall quarterly cost for EMI to ship units through TIN?
5. How many of each unit should be shipped from one planet to the next? Report this particular data in a table.
6. How could you adjust your linear program to ensure that whole units (i.e., not partial units) are shipped through the network?

Justify your answers. Clearly identify your answers