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We have $6,000 to invest in three types of financial products. If we invest x, dollars (in thousands of dollars) in the product n, where xn is a non-negative integer, then this investment returns us r, (xn) dollars with: r, (x,) = 7x1 + 2. (x, 2 1) r2(x2) = 3x2 + 7. (x2 2 1) %3D

We have $6,000 to invest in three types of financial products. If we invest x, dollars (in thousands of dollars) in the product n, where xn is a non-negative integer, then this investment returns us r, (xn) dollars with: r, (x,) = 7x1 + 2. (x, 2 1) r2(x2) = 3x2 + 7. (x2 2 1) %3D

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3CEXP
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Exercise 3: We have $6,000 to invest in three types of financial products. If we invest x„ dollars (in thousands of dollars) in the product n, where xn is a non-negative integer, then this investment returns us r„ (x„) dollars with: r, (x,) = 7x, + 2. (x, > 1) r2(x2) = 3x, + 7. (x2 2 1) r3(x3) = 4x3 + 5. (x3 2 1) rị (0) = r2 (0) = r3 (0) = 0. %3D The objective is obviously to maximize the sum of the returns on the investments. A mathematical model for this problem could be expressed as follows: Max r1 (x1) + r2 (x2) + r3 (X3) her. X1 + X2+ X3 = 6 X3 2 0 and integers, n = 1, 2, 3. We decide to tackle this problem using dynamic programming. a- Specify the steps, states, decision variables, and recurrence formula for this problem. b- Solve the problem using dynamic programming. Indicate all the steps of the resolution process and describe the optimal decision policy(ies) obtained at the end.
Transcribed Image Text:Exercise 3: We have $6,000 to invest in three types of financial products. If we invest x„ dollars (in thousands of dollars) in the product n, where xn is a non-negative integer, then this investment returns us r„ (x„) dollars with: r, (x,) = 7x, + 2. (x, > 1) r2(x2) = 3x, + 7. (x2 2 1) r3(x3) = 4x3 + 5. (x3 2 1) rị (0) = r2 (0) = r3 (0) = 0. %3D The objective is obviously to maximize the sum of the returns on the investments. A mathematical model for this problem could be expressed as follows: Max r1 (x1) + r2 (x2) + r3 (X3) her. X1 + X2+ X3 = 6 X3 2 0 and integers, n = 1, 2, 3. We decide to tackle this problem using dynamic programming. a- Specify the steps, states, decision variables, and recurrence formula for this problem. b- Solve the problem using dynamic programming. Indicate all the steps of the resolution process and describe the optimal decision policy(ies) obtained at the end.
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