Multi objective Problem of Next Investment Advisors1 A client of Next Investment Advisors ("Next") has $80,000 to invest and, as an initial strategy, would like the investment portfolio restricted to two stocks: 

Stock Price/share

U.S. Oil $25 Hub Properties $50

Estimated annual Risk

return/share

index/share

$3 (12%) 0.50 $5 (10%) 0.25

Higher risk index values implygreaterrisk; hence, Next has judged US Oil to be the riskier investment. By specifying a maximum portfolio risk index, Next will avoid placing too much of the portfolio in high-risk investments. For example, if all $80,000 are invested in the higher-risk US Oil, that would be 3,200 shares, and the portfolio would have a risk index of (3,200)(0.5) = 1,600. Conversely, if Next purchases no shares of either stock, the portfolio will have no risk, but also no return. Thus, the portfolio risk index can vary from 0 (least risk) to 1600 (most risk).

Question 1: Download the spreadsheetNext Investment Advisors TEMPLATE.xlsx.2Input the Solver parameters for the single objective "minimize risk index" (cell D15). What dollar return and what risk index are produced?

Question 2: Copy the tab to replicate the spreadsheet. Rename this new tab "max return." Change the Solver parameters to reflect the other objective, "maximize return" (cell D14). What dollar return and what risk index are produced?

Neither extreme identified in Q1 and Q2 are exactly what the client wants. Next's client would like to avoid a high-risk portfolio; thus, investing all funds in US Oil is not

1This case appeared in Anderson, Sweeney, and William'sAn Introduction to Management Science(Thomson/Southwestern, 2003). The questions were prepared by William P. Millhiser for the Zicklin School of Business as the basis for class discussion rather than to illustrate either effective or ineffective handling of an administrative decision. This document is copyright 2021 by William P. Millhiser, and may not be distributed, shared, or posted in any way without explicit written consent. 2A spreadsheet model of this problem is available for download. See Blackboard > MGT 3500 > Cases 11-15 > Mini Case 14 > 7-3 Next Investment Advisors TEMPLATE.xlsx.

desirable. However, the client agreed that an acceptable level of risk would correspond to portfolios with a total risk index of 700. It is equally undesirable to be above or below 700.Thus, considering only risk, one goal is to find a portfolio with a risk index as close to 700 as possible.

Another goal of the client is to obtain an annual return of at least $9000. This goal can be achieved with a portfolio consisting of 2000 shares of US Oil and 600 shares of Hub Properties; the annual return would be 2000($3)+600($5) = $9000. The portfolio risk index would be 2000(0.5)+600(0.25) = 1150; thus, this portfolio achieves the annual return goal but does not satisfy the portfolio risk index goal.

The client's top priority is to restrict risk; that is, keeping the portfolio risk index at 700 is seen as 3 times more important than obtaining the $9000 return. Specifically, every 1 risk unit that the portfolio deviates from 700 is 3 times worse than every $1 shortfall below a $9000 return.

Question 3: Given the penalties implied in the prior paragraph, compute the number of total penalty points for the solution obtained in Q1 and Q2.

Question 4: Copy the model into a 3rdtab in the spreadsheet (rename the tab "goal prgm"). Formulate this problem as a goal program to help Next properly advise the client. You will need to add 2 goal constraints and add the penalties and compute the total penalty for any feasible solution. How should the $80,000 be divided between the two stocks?