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Unformatted text preview: guarantee that j x is positive for at least one j, say, for j = 2. The equation 2 2 2 x a 2 b = demonstrates that is positive and that 2 2 2 a 2 b x = . And the equation that is complementary to j x guarantees (1) j j j a 2 b x = for j = 1, 2, , m . Multiply equation (1) by j b , sum over j, and then substitute into the constraint of the nonlinear program to see that ] a / ) b [( 200 k m 1 k 2 k = = , and then use (1) to see that the optimal solution to this nonlinear program is ] a / ) b [( a / b 100 x k m 1 k 2 k j j j = = for j = 1, 2, , m ....
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- Fall '10