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# hw4 - Design Analysis of Algorithms HW 4 Submission date...

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Submission date: 22.01.2009 14:00 1. A truck owner is performing a delivery from Haifa to Eilat. The truck has three containers in the front, middle and back of the truck. The sizes and of the containers (in cubic meters) are: Front 70 Middle 90 Back 50 The weights in Kg that can be carried in each container are: Front 2000 Middle 3200 Back 1600 There are four types of material to be shipped: Type Weight (Kg) Volume (cubic meter/1000Kg) Proﬁt (\$/Kg) T1 3600 50 200 T2 3000 70 250 T3 4500 60 220 T4 2200 40 230 (a) How should the driver load her truck in order to maximize her proﬁt from the delivery? Formulate this as a linear program. (b) Suppose that the truck must be balanced, so that the weight in each container divided by the maximal weight in the container should be the same proportion for all three compartments. Can you extend the LP from part (a) to one that will guarantee this as well? If so, give the new LP, and if not, explain why. 2. Formulate the dual of the following linear program:

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hw4 - Design Analysis of Algorithms HW 4 Submission date...

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