E160 Operations Research I
Fall 2008
Homework #2 Solution
Chapter 12
Section 12.2
1. Let
S = soap opera ads and F = football ads. Then we wish
to
min z = 50S + 100F
st
5S
1/2
+ 17F
1/2
≥
40 (men)
20S
1/2
+ 7F
1/2
≥
60 (women)
S
≥
0, F
≥
0
9.Let Wi = number of widgets produced at plant I.
max 10*(W1+W2)20*W1^.540*W2^.333;
s.t. W1<70;
W2<70;
W1+W2<120;
W1>.01;
W2>.01;
11. We let TIME and TEMPER be original values of variables,
and T and TEMP be normalized values. variable names.
max  1.4 * T + .4 * TEMP  2.2 * T ^ 2  3.2 * TEMP ^ 2  4.9 * T
* TEMP ;
s.t
T = ( TIME  90 ) / 10 ;
TEMP = ( TEMPER  150 ) / 5 ;
TIME >= 60 ;
TIME <= 120 ;
TEMPER >= 100 ;
TEMPER <= 200 ;
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;
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 Spring '08
 ADLER
 Operations Research, Heat, heating oil

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