f07hw1soln_1_-1 - 1. Let the decision variables be the...

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Unformatted text preview: 1. Let the decision variables be the following: x i is the percentage of SM- i in the mixture, i = 1 , . . . , 4. The solution is then x = . 25 . 34 . 39 . 02 . The solution to the system of equations is unique since the rank of the coefficient matrix is equal to the number of unknowns, i.e. 4. In this case, the solution to the system of equations satisfies the nonnegativity restrictions. See below for the Matlab solution. octave:1> A=[5 7 2 1; 3 6 1 2; 4 5 3 1; 88 82 94 96; 1 1 1 1] A = 5 7 2 1 3 6 1 2 4 5 3 1 88 82 94 96 1 1 1 1 octave:2> b=[4.43; 3.22; 3.89; 88.46; 1] b = 4.4300 3.2200 3.8900 88.4600 1.0000 octave:3> x=A\b x = 0.250000 0.340000 0.390000 0.020000 octave:4> A=[5 7 2 1; 3 6 1 2; 4 5 3 1; 88 82 94 96] A = 5 7 2 1 1 3 6 1 2 4 5 3 1 88 82 94 96 octave:5> b=[4.43; 3.22; 3.89; 88.46] b = 4.4300 3.2200 3.8900 88.4600 octave:6> x=A\b x = 0.250000 0.340000 0.390000 0.020000 Notice that the solution is the same regardless of including the summation constraint equal...
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f07hw1soln_1_-1 - 1. Let the decision variables be the...

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