ESI 6314 Deterministic Methods in Operations Research
Fall 2010
HW 3 Solutions
Problems 13, page 231
1. Typical isoprofit line is 3x
1
+c
2
x
2
=z. This has slope 3/c
2
. If slope of isoprofit line is <2, then Point
C is optimal. Thus if 3/c
2
<2 or c
2
<1.5 the current basis is no longer optimal. Also if the slope of the
isoprofit line is >1 Point A will be optimal. Thus if 3/c
2
>1 or c
2
>3 the current basis is no longer
optimal. Thus for 1.5
≤
c
2
≤
3 the current basis remains optimal.
For c
2
= 2.5 x
1
= 20, x
2
= 60, but z = 3(20) + 2.5(60) = $210.
2. Currently Number of Available Carpentry Hours = b
2
= 80. If we reduce the number of available
carpentry hours
we see that when the carpentry constraint moves past the point (40, 20) the
carpentry and finishing hours constraints will be binding at a point where x
1
>40. In this situation
b
2
<40 + 20 = 60.
Thus for b
2
<60 the current basis is no longer optimal. If we increase the number of
available carpentry hours we see that when the carpentry constraint moves past (0, 100) the carpentry
and finishing hours constraints will both be binding at a point where x
1
<0. In this situation b
2
>100.
Thus if b
2
>100 the current basis is no longer optimal. Thus the current basis remains optimal for
60
≤
b
2
≤
100. If 60
≤
b
2
≤
100, the number of soldiers and trains produced will change.
3. If b
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 Fall '09
 VLADIMIRLBOGINSKI
 Optimization, Confectionery, candy bar, If and only if, Logical biconditional

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