Asked by brent ashley on Jul 13, 2024
Verified
A financial advisor is about to build an investment portfolio for a client who has $100,000 to invest. The four investments available are A, B, C, and D. Investment A will earn 4% and has a risk of two "points" per $1,000 invested. B earns 6% with 3 risk points; C earns 9% with 7 risk points; and D earns 11% with a risk of 8. The client has put the following conditions on the investments: A is to be no more than one-half of the total invested. A cannot be less than 20% of the total investment. D cannot be less than C. Total risk points must be at or below 1,000.Identify the decision variables of this problem. Write out the objective function and constraints. Do not solve.
Investment Portfolio
A collection of stocks, bonds, or other investment vehicles chosen by an individual or institution to achieve specific financial goals.
Objective Function
A mathematical function used in optimization to define the goal of the optimization problem, typically involving the maximization or minimization of some quantity.
Decision Variables
Variables that decision-makers control in optimization problems, representing choices available to achieve the desired outcome.
- Engage linear programming for practical decision-making applications, recognizing decision variables, objective functions, and boundaries.
- Develop constraints for linear programming (LP) based on verbal descriptions.
Verified Answer
Subject to
A + B + C + D = $100,000
.5A - .5B - .5C -.5D ≤ 0 (rearranged from A ≤ .5(A + B + C + D))
.8A - .2B - .2C - .2D ≥ 0 (rearranged from A ≥ .2 (A + B + C + D))
-C + D ≥ 0 (rearranged from D ≥ C)
.002A + .003B + .007C + .008C ≤ 1000
Learning Objectives
- Engage linear programming for practical decision-making applications, recognizing decision variables, objective functions, and boundaries.
- Develop constraints for linear programming (LP) based on verbal descriptions.
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