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# sfin03 - 11[20 points Consider the problem Minimize f(1 =...

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Unformatted text preview: 11. [20 points] Consider the problem Minimize f(1) = f(\$1, \$2, \$3) = :sz + x3 + 55% subject to \$1—2I172+3.'133 = 4 1172+ \$3 = 1 (a) Find a feasible solution 37: to the problem. (b) Find a null—space matrixfor the matrix A of coefﬁcients of the constraint equations. ((1) Use parts (a) and (b) to write the reduced equation 45(1)) (Whose unconstrained local minimizers are the local 'minimizers of the given problem) as a polynomial in 11. 12. [15 points] Suppose 93* is an optimal solution to the linear programming problem in standard form: Minimize z = ch subject to Ax = b,:r 2 0 and suppose the variables have been reordered so that A = [B N] Where the B corresponds to the optimal basis. Letting y* = (B‘1)TcB, prove that cTw* = bTy*. ...
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