Formulate a linear programming problem that can be used to solve the following question. Suppose for an investment no more than $16,000 is placed in three mutual funds with annual returns of 3%, 6%, and 10%, respectively. The investor requires an annual return of at least $960 and wishes to minimize the risk. The second mutual fund is twice as risky as the first, and the third is 4 times as risky as the first. How should the money be allocated to minimize the risk?
Formulate a linear programming problem that can be used to solve the following question. Suppose for an investment no more than $16,000 is placed in three mutual funds with annual returns of 3%, 6%, and 10%, respectively. The investor requires an annual return of at least $960 and wishes to minimize the risk. The second mutual fund is twice as risky as the first, and the third is 4 times as risky as the first. How should the money be allocated to minimize the risk?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Formulate a linear programming problem that can be used to solve the following question.
Suppose for an investment no more than $16,000 is placed in three mutual funds with annual returns of 3%, 6%, and 10%, respectively. The investor requires an annual return of at least $960 and wishes to minimize the risk. The second mutual fund is twice as risky as the first, and the third is 4 times as risky as the first. How should the money be allocated to minimize the risk? Let risk = x1 + 2x2 + 4x3.
x1 = amount of money in dollars invested in the first fund
x2 = amount of money in dollars invested in the second fund
x3 = amount of money in dollars invested in the third fund
| ---Select--- Maximize Minimize | F =
|
(objective function) |
| Subject to |
|
(dollars available) |
|
|
(total investment return) | |
|
x1 ---Select--- ≤ > < = ≥ 0, x2 ---Select--- = > ≤ < ≥ 0, x3 ---Select--- ≤ < = ≥ > |
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