hw03solutions

# hw03solutions - IEOR 162 Linear Programming Spring 2007...

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Unformatted text preview: IEOR 162 Linear Programming Spring 2007 Homework 3 Solutions 3.8.9 (4 points) Data: I = set of possible investments (i.e. the four bonds) W = initial total wealth (i.e. \$1,000,000) r i = expected return from investment i ∈ I (i.e. 1.13 for investment 1) w i = worst case return from investment i ∈ I d i = duration of investment i ∈ I Variables: x i = amount to invest in investment i ∈ I Formulation: max ∑ i ∈ I r i x i s.t. ∑ i ∈ I w i x i ≥ 1 . 08 ∑ i ∈ I x i , (1) ∑ i ∈ I d i x i ≤ 6 ∑ i ∈ I x i , (2) x j ≤ . 4 ∑ i ∈ I x i , j ∈ I (3) ∑ i ∈ I x i ≤ W, (4) x i ≥ , i ∈ I Constraints 1-3 correspond to the constraints listed for the problem. Constraint 4 ensures that we don’t spend more than the amount we have to invest. The objective maximizes total expected return. 3.10.5 (4 points) Data: V = set of vehicles to produce (i.e. { trucks,cars } ) d it = demand for vehicles of type i ∈ V during month t M = maximum number of vehicles produced in a month s i = amount of steel used by one vehicle of type i ∈ V c t = cost of steel during month t N = maximum amount of steel available for purchase each month I i = initial inventory for vehicle type...
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hw03solutions - IEOR 162 Linear Programming Spring 2007...

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