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HW2_Sol

# HW2_Sol - E160 Operations Research I Spring 2009 Homework#2...

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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*HO-20*SQ-AG-AHO+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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HW2_Sol - E160 Operations Research I Spring 2009 Homework#2...

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