Midterm problem: You have 10,000 dollars to invest in some combination of four investments. The annual yields are 3%, 5%, 7% and 15%. Each investment has a risk rating between 1(low) and 10(high). The ratings are respectively 1, 3, 5, 10. You want to maximize your annual yield, but will tolerate an average risk per dollar invested of at most 4. [mune 96] cat test02.lp max: .03 x1 + .05 x2 + .07 x3 + .15 x4; Cap: x1 + x2 + x3 + x4 < 10000; Risk: -3 x1 - x2 + x3 + 6 x4 < 0; [mune 97] lp_solve -p < test02.lp Value of objective function: 700 x1 6666.67 x2 0 x3 0 x4 3333.33 Dual values: Cap 0.07 Risk 0.0133333 [mune 98] cat test02a.lp max: .03 x1 + .05 x2 + .07 x3 + .15 x4; Cap: x1 + x2 + x3 + x4 < 10000; Risk: -2 x1 + 2 x3 + 7 x4 < 0; [mune 99] lp_solve -p < test02a.lp Value of objective function: 566.667 x1 7777.78 x2 0 x3 0 x4 2222.22 Dual values: Cap 0.0566667 Risk 0.0133333 [mune 100] cat test02b.lp max: .03 x1 + .05 x2 + .07 x3 + .15 x4; Cap: x1 + x2 + x3 + x4 < 10000; Risk: -4 x1 - 2 x2 + 5 x4 < 0; [mune 101] lp_solve -p < test02b.lp Value of objective function: 833.333 x1 5555.56 x2 0 x3 0 x4 4444.44 Dual values: Cap 0.0833333 Risk 0.0133333