An investment advisor at Shore Financial Services wants to develop a munds, that can be was, An investment ad sands among four alternatives: stocks, bonds, mutual funds and coat, which al pected no provide an annual rate of return of 10%, 3%, 4%, and 1%, respectively. For the coming expected no period, the company developed estimates of the associated risk for each altemaine measured using an index between 0 and 1, with higher risk values denoting more volatility and the more uncertainly. The risk indices of stocks, bonds, and mutual funds are estimated to be 0.8,03 and 0.3, respectively, Because cash is held in a money market fund, the annual return is lower, but carries essentially no risk. The objective is to determine the portion of funds allocated to each investment alternative in order to maximize the total annual return for the portfolio subject to the risk level the client is willing to tolerate. Suppose the maximum risk value for a particular elient is

0.65. Shore Financial Services specified additional guidelines that must be applied to all elients. The guidelines are as follows: no more than 75% of the total investment may be in stocks; the amount invested in mutual funds must be at least as much as invested in bonds; and the amount of cash must be at least 10%, but no more than 30% of the total investment funds. Formulate the advisor's problem as an LPP.

xz=3x1+4x2x12x2150x1+3x2180x2500 2. The Porsche Club of America sponsors driver education events that provide highperformance driving instruction on actual race tracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. Deegan lndustries manufactures two types of roll bars for Porsches. Model DRB is bolted to the car using existing holes in the car's frame. Model DRW is a heavier roll bar that must be welded to the car's frame. Model DRB requires 20 pounds of a special high alloy steel, 40 minutes of manufacturing time, and 60 minutes of assembly time. Model DRW requires 25 pounds of the special high alloy steel, 100 minutes of manufacturing time. and 40 minutes of assembly time. Deegan's steel supplier indicated that at most 40,000 pounds of the high-alloy steel will be available next quarter. In addition, Decgan estimates that 2000 hours of manufacturing time and 1600 hours of assembly time will be available next quarter. The profit contributions are $200 per unit for model DRB and $280 per unit for model DRW. The computer solution is shown in the following figure: xz=3x1+4x2x12x2150x1+3x2180x2500 2. The Porsche Club of America sponsors driver education events that provide highperformance driving instruction on actual race tracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. Deegan lndustries manufactures two types of roll bars for Porsches. Model DRB is bolted to the car using existing holes in the car's frame. Model DRW is a heavier roll bar that must be welded to the car's frame. Model DRB requires 20 pounds of a special high alloy steel, 40 minutes of manufacturing time, and 60 minutes of assembly time. Model DRW requires 25 pounds of the special high alloy steel, 100 minutes of manufacturing time. and 40 minutes of assembly time. Deegan's steel supplier indicated that at most 40,000 pounds of the high-alloy steel will be available next quarter. In addition, Decgan estimates that 2000 hours of manufacturing time and 1600 hours of assembly time will be available next quarter. The profit contributions are $200 per unit for model DRB and $280 per unit for model DRW. The computer solution is shown in the following figure