IEOR 162 LINEAR PROGRAMMING (FALL 04)
HOMEWORK 3 SOLUTIONS
3.3.8.
The LP is infeasible, because no points can satisfy the last two
constraints.
3.3.10.
Let x1 = dollars bought (for francs) and x2 = francs bought (for
dollars). Then we wish to solve
max z = x1  .25x2
st
x1  .25x2
≥
0 (dollar constraint)
3x1 + x2
≥
0 (franc constraint)
x1, x2
≥
0
In the graph the LP's feasible region is between the lines
indicated by segments AB and AC. Isoprofit lines are parallel to
AB. We increase z by moving down and to right. Since AB has a
larger slope than AC, we will have an unbounded LP. This is due to
the inconsistency in the exchange rate in the FranceUSA market.
Of course, such an inconsistency in the currency markets would
quickly be corrected before you could make an infinite amount of
money!
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3.4.1.
For i = 1, 2, 3 let x
i
= Tons of processed Factory i waste.
Then appropriate LP is
min z =
15x
1
+ 10x
2
+ 20x
3
s.t.
.10x
1
+ .20x
2
+ .40x
3
≥
30(Pollutant 1)
.45x
1
+ .25x
2
+ .30x
3
≥
40(Pollutant 2)
x
1
≥
0,x
2
≥
0,x
3
≥
0
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 Fall '07
 Zhang
 1 ton, 3 pounds, 10 tons

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