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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 Spring '10
 H.F.
 Algorithms, linear program, polynomial time, T2 T3 T4

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