The Module 6 Final Project consists of two parts. If using Excel, complete each part in a separate           worksheet of the same Excel workbook (Name your worksheets:“Part 1”and“Part 2”). If using R,       complete each part in a separate R script file. The submission of this project will consist of an Excel      workbook (or two R script files if R has been used) and a Word document. For each part, write a        minimum of 1500 words in the Word document describing your methods and your findings.                 Furthermore, the Word document should be according to the APA standards, i.e., it consists of a title  page (including student’s name, assignment title, course number and title, the current academic term,    instructor’s name, and the assignment completion date), and a reference page. The Word submission of each project will consist of three sections:

(i)         Introduction

(ii)       Analysis

(iii)       Conclusion

Part 1: Rockhill Shipping & Transport Company

Allen, a manager of the South-Atlantic office of the Rockhill Shipping & Transport Company is               negotiating a new shipping contract with Chimotoxic, a company that manufactures chemicals for          industrial use. Chimotoxic wants Rockhill to pick up and transport waste products from its six plants to three waste disposal sites. Allen is very concerned about this proposal arrangement. The chemical        wastes that will be hauled can be hazardous to humans or the environment if they leak. In addition,       some of the communities in the regions where the plants are located may prohibit hazardous materials from being shipped through their municipal limits. Thus, not only the shipments have to be handled       carefully and transported at reduced speeds, but they may also have to traverse in circuitous routes in  some cases.

Allen has estimated the cost of shipping a barrel of waste from each of the six plants to each of the three waste disposal sites as shown in the following table.

Table 1: Shipping costs, per barrel of waste from six plants to three waste disposal sites

The plants generate the following amounts of waste products each week:

Table 2: Total Waste generated by each plant

The three waste disposal sites at Orangeburg, Florence, and Macon can respectively accommodate a maximum of 65, 80, and 105 barrels per week.

In addition to shipping directly from each of the six plants to one of the three waste disposal sites, Allen is also considering using each of the plants and the waste disposal sites as intermediate shipping points.  In this case, trucks would be able to drop a load at a plant or a disposal site to be picked up and carried on to the final destination by another truck. Furthermore, Rockhill would not incur any handling costs   because Chimitoxic has agreed to take care of all the handling costs at the plants and at the disposal      sites. In other words, Rockhill’s only cost will be the transportation cost. Therefore, Allen wants to be  able to consider the possibility that it may be cheaper to drop and pick up loads at intermediate points  rather than ship them directly.

Allen has estimated the shipping costs per barrel between each of the six plants to be as follows:

Table 3: Shipping costs, per barrel of waste from each plant to another plant

The estimated shipping cost per barrel between each of the waste disposal sites is as follows:

Table 4: Shipping costs, per barrel of waste between the three waste disposal sites

Allen wants to determine the shipping routes that will minimize Rockhill’s total cost in order to develop a contract proposal to submit to Chimotoxic for waste proposal. He particularly wants to know if it      would be cheaper to ship directly prom the plants to the waste sites or if he should drop and pick up    some loads at the various plants and waste sites.

In the word document, explain the details of the solutions obtained for the optimal routes and their

respective optimal costs for both cases. In particular for the case when loads are dropped and picked up at various plants and waste sites, explain how many barrels, in total, will be transported each week from a source to a destination.

Part 2: Investment Allocations

An investor has selected the following asset types in his portfolio. The expected return for each asset

type has been estimated by using the historical data:

Expected Returns

Table 5: Expected returns of Investments

The following table indicates the covariance matrix of the assets’returns. Each diagonal entry is the variance of an asset and non-diagonal entries are the covariances between any pairs of assets.

Bonds

High tech stocks Foreign stocks  Call options  Put options Gold

(i)

(ii)

Call options    Put options         Gold

Table 6: The Covariance matrix of assets’returns

Suppose that our investor wishes to invest $10,000 in this portfolio. Determine how he     should allocate this investment to the individual assets in his portfolio in order to have a     minimum baseline expected return of 11%, and at the same time, at a minimum risk.           Let the solution pair be denoted by (r, e), where“r”denotes the minimized risk and“e”   denotes the expected portfolio return after the problem is solved. Use successive values of 10%, 10.5%, 11%, 11.5%, 12%, 12.5%, 13% and 13.5% as the baseline return values to obtain

eight pairs of solutions (r, e).  Plot“e”versus“r”. Explain whether there exists a pattern in   this plot. In other words, explain, in your opinion, the type of mathematical relationship that “r”and“e”may have.