1. An investment broker has been given $250,000 to invest in a 12-month commitment. The money can be placed in Treasury notes (with a return of 8% and a risk score of 2) or in municipal bonds (with a return of 9% and a risk score of 3). The broker’s client wants diversification to the extent that between 50% and 70% of the total investment must be placed in Treasury notes. Also, because of fear of default, the client requests that the average risk score of the total investment should be no more than 2.42. How much should the broker invest in each security so as to maximize return on investment?
2. A plumbing manufacturer makes two lines of bathtubs, model A and model B. Every tub requires blending a certain amount of steel and zinc; the company has available a total of 24,500 pounds of steel and 6,000 pounds of zinc. Each model A bathtub requires a mixture of 120 pounds of steel and 20 pounds of zinc, and each yields a profit of $90. Each model B tub produced can be sold for a profit of $70; it requires 100 pounds of steel and 30 pounds of zinc. To maintain an adequate supply of both models, the manufacturer would like the number of model A tubs made to be no more than 5 times the number of model B tubs. Find the best product mix of bathtubs.