5. An investment firm has just been instructed by one of its clients to invest $1,500,000...

 

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5. An investment firm has just been instructed by one of its clients to invest $1,500,000 of his money. The client's goal is to maximize total projected return on investments. The analysts at the firm are considering the following options for investment: Investment Option Company A stocks Company B stocks Company C stocks Company D stocks Projected Rate of Return (%) 14.2 8.4 7.0 5.0 Risk (%) 2.6 1.6 1.2 0.4 The client has specified the following guidelines: - The total risk should be less than or equal to $20,000. - Company D stock should constitute at least 10% of the money invested. At least 50% of the funds available should be placed in a combination of company A, B, and C stocks. - No more than 30% of the amount invested in company C stocks should be invested in company A stock. Formulate a linear optimization model for this investment problem. (a) Define the decision variables. (b) Determine the objective function. What does it represent? (c) Determine all the constraints. Briefly describe what each constraint represents. Note: Do NOT solve the problem aftor formulating 5. An investment firm has just been instructed by one of its clients to invest $1,500,000 of his money. The client's goal is to maximize total projected return on investments. The analysts at the firm are considering the following options for investment: Investment Option Company A stocks Company B stocks Company C stocks Company D stocks Projected Rate of Return (%) 14.2 8.4 7.0 5.0 Risk (%) 2.6 1.6 1.2 0.4 The client has specified the following guidelines: - The total risk should be less than or equal to $20,000. - Company D stock should constitute at least 10% of the money invested. At least 50% of the funds available should be placed in a combination of company A, B, and C stocks. - No more than 30% of the amount invested in company C stocks should be invested in company A stock. Formulate a linear optimization model for this investment problem. (a) Define the decision variables. (b) Determine the objective function. What does it represent? (c) Determine all the constraints. Briefly describe what each constraint represents. Note: Do NOT solve the problem aftor formulating