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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 $6,000 is placed in three mutual funds with annual returns of 3%, 7%, and 11%, respectively. The investor requires an annual return of at least $450 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 Minimize F = (objective function) Subject to (dollars available) (total investment return) X1 < |× 0, x2 3 V× 0, x3 = Additional Materials O eBook

Formulate a linear programming problem that can be used to solve the following question. Suppose for an investment no more than $6,000 is placed in three mutual funds with annual returns of 3%, 7%, and 11%, respectively. The investor requires an annual return of at least $450 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 Minimize F = (objective function) Subject to (dollars available) (total investment return) X1 < |× 0, x2 3 V× 0, x3 = Additional Materials O eBook

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 3SC: In Example 3, if the accountant earns a profit of 100 on each individual return and a profit of 175...
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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 $6,000 is placed in three mutual funds with annual returns of 3%, 7%, and 11%, respectively. The investor requires an annual return of at least $450 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 Minimize F = (objective function) Subject to (dollars available) (total investment return) X1< 0, x2 s × 0, x3 = %3D Additional Materials еВook
Transcribed Image Text:Formulate a linear programming problem that can be used to solve the following question. Suppose for an investment no more than $6,000 is placed in three mutual funds with annual returns of 3%, 7%, and 11%, respectively. The investor requires an annual return of at least $450 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 Minimize F = (objective function) Subject to (dollars available) (total investment return) X1< 0, x2 s × 0, x3 = %3D Additional Materials еВook
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