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Question 2 (2 marks): An investment agency has been asked to advise one of its clients how to invest his $100,000 among the 4 assets described below: Assets Northern Mines Shares Bucklin Automobiles Royal Bank of Commerce Shares NB Savings Bonds Units of Risk per Dollar Invested 4 3.5 2 1 Rate of Return .15 .11 .07 .05 The client would like as high an annual return as is possible to receive while incurring of an average of no more than 2.5 risk units per dollar invested. The amount invested in Royal Bank cannot exceed $40,000. Furthermore, the investment in Automobiles and Banks combined must be at least $20,000. (a) Formulate the problem as a linear programming problem (regular or LINDO/LINGO format). Define the variables properly & clearly. What is the optimal solution & what is the average rate of return? (b) If we could borrow some additional funds at 11%, would it be worth our while? Explain in one short sentence. (c) There is a rumor that the return of the Royal Bank will increase to 8%. Will this change the investor's plans? What if it decreases to 5.5%? Explain in one short sentence. (d) What if the rate of return for Bucklin Automobiles were to decrease to 9%? Will that change our plans? What if increases to 13%? Explain in one short sentence. Solution: Question 2 (2 marks): An investment agency has been asked to advise one of its clients how to invest his $100,000 among the 4 assets described below: Assets Northern Mines Shares Bucklin Automobiles Royal Bank of Commerce Shares NB Savings Bonds Units of Risk per Dollar Invested 4 3.5 2 1 Rate of Return .15 .11 .07 .05 The client would like as high an annual return as is possible to receive while incurring of an average of no more than 2.5 risk units per dollar invested. The amount invested in Royal Bank cannot exceed $40,000. Furthermore, the investment in Automobiles and Banks combined must be at least $20,000. (a) Formulate the problem as a linear programming problem (regular or LINDO/LINGO format). Define the variables properly & clearly. What is the optimal solution & what is the average rate of return? (b) If we could borrow some additional funds at 11%, would it be worth our while? Explain in one short sentence. (c) There is a rumor that the return of the Royal Bank will increase to 8%. Will this change the investor's plans? What if it decreases to 5.5%? Explain in one short sentence. (d) What if the rate of return for Bucklin Automobiles were to decrease to 9%? Will that change our plans? What if increases to 13%? Explain in one short sentence. Solution
