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Unformatted text preview: IE398.Final Exam Name: ? n>t L. 1.1 Problem (10 points) Formulate a LP to minimize the total cost of meeting the next three months' demands for each type of cake. .[ +'f'~ (.,h'G Answer. 0\ , ,..... ~ r v " l S. b".r~') du nt\., ti N'e t:~, Lt..\ .;. ~ Q\ C:G\~~ ~ ( ...J ~ f..rx L (t c C ~ t e~J : . I I\'HA\{~'/ /)f (A{es 0\ ~ F .Lc~ , J ~)J teT ~ ffit(\ .'L i C) r:jt + _1 L OJIJ' J&C tfT JEC 't;"'\ 5.1= , 'Xjl = clj\ + Ijl \f JEL. Ij ItI t /CJ1: : J.1t +rj t 'If jE C vttT\tI1. 1':t, J d'~ J Ajt ,rjl. ~o \fj~c.. '1~(=,f . . . IE398 Final Exam Name: ?~f. L 1.2 Problem (15 points) Suppose that in any month Lee Sara has the option of not meeting demand. However, he must pay a penalty cost of $3.60 for each cheesecake by which he does not meet his demand, and $3.00 for each Black Forest cake by which he does not meet demand. (Parameter people: Let O!j,j E C, be the percake penalty that Lee Sara must pay for not meeting demand for cake type j.) Formulate a LP to minimize the total cost of meeting the next three months' demands for each type of cake plus the penalty costs for not meeting this demand. Answer. T".h1)J.,L ~ ~ob~ 'Ijt = t ~Q.~ o~ +tpe j&c.. ~r ~()to fe\Lt..t de,rtIAJ I~ t E:T . S J "'t = S~(f1' CtS"'" c.. r _r II! r i~ t E ~ 0.( C4;y~~dT ~r' ~6 '" ~ fA ?:Gturt ' ~ ~\ jl \i ?rj~ 1~~)~=\V tY\r ( r\ ~ L:~<t "(tdj TOt + dj Sjt) J J ,J J Jf:G t~, s.t. 1jl jl 1" Tj\ 'JJc.. T)fH +rjt:c 1jt +:rjt \fjtC) \I t" \ f IJ jr T Sjt djt \/JtcC) Vtce\ (*) "Kjt( jt( Tjt( 5jt V J f; C ) IJ f;:E'\ , IE398 Final Exam Name: 1.3 Problem (10 points) Suppose that Lee Sara can only let his demand slip by 5 at the penalty costs described in Problem 1.2. If his demand slips by more than 5, he must pay the larger penalty costs of $4.60 for each cheesecake and $3.50 for each Blackcosts of $4....
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This note was uploaded on 02/29/2008 for the course IE 426 taught by Professor Linderoth during the Spring '08 term at Lehigh University .
 Spring '08
 Linderoth

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