hw09solutions

hw09solutions - Data: p i = purchase price for stock i c i...

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IEOR 162 Linear Programming Spring 2007 Homework 9 Solutions 6.5.3 (4 points) Dual: min 5 y 1 + 7 y 2 + 6 y 3 + 4 y 4 s.t. y 1 + 2 y 2 + y 4 4 y 1 + y 2 + 2 y 3 = - 1 y 3 + y 4 = 2 y 1 , y 2 0 , y 3 0 , y 4 urs 6.7.2 a. (2 points) Dual: min 3 y 1 + 2 y 2 + y 3 s.t. y 1 + y 3 ≥ - 2 y 1 + y 2 ≥ - 1 y 1 + y 2 + y 3 1 y 1 0 , y 2 0 , y 3 urs b. (2 points) Optimal Dual Solution: y 1 = 0 , y 2 = - 1 , y 3 = 2. 6.7.3 (3 points) Optimal dual solution is y 1 = . 4 , y 2 = 1 . 4, so optimal objective value is z * = . 4( . 5) + 1 . 4( . 5) = . 9. 6.7.5 (4 points) Optimal dual solution is y 1 = 0 , y 2 = 1 so the optimal objective value should be z * = 0(6) + 1(10) = 10 6 = 20 3 . Strong duality tells us that the optimal objective values of the primal and dual must be equal, so the computations must have been done incorrectly. 3.review.45 (5 points) AMPL Files available via class website
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Unformatted text preview: Data: p i = purchase price for stock i c i = current price for stock i v i = expected value in 1 year for stock i Variables: x i = number of shares to sell of stock i Formulation: max ∑ 10 i =1 (100-x i ) v i s.t. ∑ 10 i =1 ( c i x i-. 3( c i-p i ) x i-. 01 c i x i ) ≥ 30 , 000 (1) x i ≤ 100 x i ≥ The objective is to maximize the expected value of the stock remaining in 1 year. Constraint 1 ensures that we get $30,000 from selling stock minus the transaction costs and taxes. 1...
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This homework help was uploaded on 04/02/2008 for the course IEOR 162 taught by Professor Zhang during the Spring '07 term at Berkeley.

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