Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client's needs. For a new client, Innis has been authorized to invest up to $1.3 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10% ; each unit of the money market fund costs $100 and provides an annual rate of return of 4%. The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $67,000. According to Innis' risk measurement system, each unit invested in the stock fund has a risk index of 14, and each unit invested in the money market fund has a risk index of 5; the higher risk index associated with the stock fund simply indicates that it is the riskier investment. Innis's client also specified that at least $750,000 be invested in the money market fund. (a) Determine how many units of each fund Innis should purchase for the client to minimize the total risk index for the portfolio. (Assume S is the number of units purchased in the stock fund and M is the number of units purchased in the money market fund.) (S, M) = (b) How much annual income (in dollars) will this investment strategy generate? $ (c) Suppose the client desires to maximize annual return and no longer requires that $750,000 be invested in the money market fund. How should the funds be invested? O Invest everything in the stock fund. O Invest half in the stock fund and half in the money market fund. Invest everything in the money market fund.
Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client's needs. For a new client, Innis has been authorized to invest up to $1.3 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10% ; each unit of the money market fund costs $100 and provides an annual rate of return of 4%. The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $67,000. According to Innis' risk measurement system, each unit invested in the stock fund has a risk index of 14, and each unit invested in the money market fund has a risk index of 5; the higher risk index associated with the stock fund simply indicates that it is the riskier investment. Innis's client also specified that at least $750,000 be invested in the money market fund. (a) Determine how many units of each fund Innis should purchase for the client to minimize the total risk index for the portfolio. (Assume S is the number of units purchased in the stock fund and M is the number of units purchased in the money market fund.) (S, M) = (b) How much annual income (in dollars) will this investment strategy generate? $ (c) Suppose the client desires to maximize annual return and no longer requires that $750,000 be invested in the money market fund. How should the funds be invested? O Invest everything in the stock fund. O Invest half in the stock fund and half in the money market fund. Invest everything in the money market fund.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 107P
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Transcribed Image Text:Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client's needs. For a new client,
Innis has been authorized to invest up to $1.3 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and
provides an annual rate of return of 10%; each unit of the money market fund costs $100 and provides an annual rate of return of 4%.
The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $67,000. According to Innis' risk
measurement system, each unit invested in the stock fund has a risk index of 14, and each unit invested in the money market fund has a risk index of 5; the
higher risk index associated with the stock fund simply indicates that it is the riskier investment. Innis's client also specified that at least $750,000 be invested in
the money market fund.
(a) Determine how many units of each fund Innis should purchase for the client to minimize the total risk index for the portfolio. (Assume S is the number of
units purchased in the stock fund and M is the number of units purchased in the money market fund.)
(S, M) =
(b) How much annual income (in dollars) will this investment strategy generate?
(c) Suppose the client desires to maximize annual return and no longer requires that $750,000 be invested in the money market fund. How should the funds
be invested?
Invest everything in the stock fund.
Invest half in the stock fund and half in the money market fund.
Invest everything in the money market fund.
OOO
Expert Solution
Step 1
| Minimize Z = 14 S + 5 M |
| subject to |
| 50 S + 100 M <= 1300000 authorized investment |
| 10% of 50 S + 4% of 100 M >= 67000 desired minimum return |
| 100 M >= 750000 minimum investment in the money market |
| S, M >= 0 |
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