E160 Operations Research I
Spring 2009
Homework #2 Solution
Chapter 12
Section 12.2
12. Let G = barrels of gas produced (with original oils) and
sold, HO = barrels of heating oil produced (with original
oils) and sold, AG = dollars spent advertising gas, AHO =
dollars spent advertising heating oil, Gi = barrels of oil i
used to make gas, HOi = barrels of heating oil i used to make
heating oil, SQG = barrels of SQ added to gas, SQHO = barrels
of SQ added to heating oil. SQ = barrels of SQ added.
max 25*G+20*HO20*SQAGAHO+25*SQG+20*SQHO;
G1+HO1<=5000;
G2+HO2<=10000;
(10*G1+5*G2)/(G)+SQG^.5>=8;
(or ((10*G1+5*G2)/(G))*(1+SQG^.5)>=8)
(10*HO1+5*HO2)/(HO)+.6*SQHO^.6>=6;
(or((10*HO1+5*HO2)/(HO))(1+.6*SQHO^.6)>=6)
AG=.2*G;
AHO=.1*HO;
SQ=SQG+SQHO;
G=G1+G2;
HO=HO1+HO2;
SQG<=.05*G; (or SQG<=0.05*(G+SQG))
SQHO<=.05*HO; (or SQHO<=0.05*(HO+SQHO))
13. Let Wi = dollars paid by Fuller brush to salesperson if
size of sale is a thousand dollars.
Min
.3 * W0
+ .2 * W5 + .5 * W50
;
s.t. .3 * W0^(1/2) + .2 * W5^(1/2) + .5 * W50^(1/2)  50 >=
20 ;
.3 * W0^(1/2) + .2 * W5^(1/2) + .5 * W50^(1/2)  50
> .6 * W0^(1/2) + .3 * W5^(1/2) + .1 * W50^(1/2) ;
W0 >= 0 ;
W5 >= 0 ;
W50 >= 0 ;
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Section 12.4
1. Let f(x) = profit if $x is spent on advertising. Then
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 Spring '07
 HOCHBAUM
 Operations Research, Optimization, heating oil, Fuller brush, SQ added. max, original oils

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