Formulate a linear programming problem that can be used to solve the following question. Suppose for an investment no more than $11,000 is placed in three mutual funds with annual returns of 4%, 8%, and 11%, respectively. The investor requires an annual return of at least $770 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 F = (objective function) Subject to (dollars available) (total investment return) x1 0, x2 0, x3 0
Formulate a linear programming problem that can be used to solve the following question. Suppose for an investment no more than $11,000 is placed in three mutual funds with annual returns of 4%, 8%, and 11%, respectively. The investor requires an annual return of at least $770 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 F = (objective function) Subject to (dollars available) (total investment return) x1 0, x2 0, x3 0
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 $11,000 is placed in three mutual funds with annual returns of 4%, 8%, and 11%, respectively. The investor requires an annual return of at least $770 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
| F =
|
(objective function) | |
| Subject to |
|
(dollars available) |
|
|
(total investment return) | |
| x1 0, x2 0, x3 0 |
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