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Unformatted text preview: IE398 Final Exam Name: ? n)~ 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. r t't,t vbV Answer. 0\ , [ v" l c. b.Kt.s Lt.\ ry ;. $I; u'l COI"t! ~ , J. ~ f'Cl:: (" ::: . ' f\,(Ulkar\.{ i)t e<>.\(e5 0\ t~ f ..lL \CJ J ~)J t<? T dun'J ti ~ tC21 c~ C ttr etlJ < rt\ l(\ ."L i Cjtcr:j+ + ,11 OJIjt JE:C tfT J~C 'tc'"\ 5.1= ~ 'Xj\ ~ dJ' + Ij\ If J~C Ij ItI t ((jt = d~t + Tj t \fj&C vte T \ t 11 , Ajt ,~jt ~o \fj"C 'if+.(::'\ . ')'"t. J d<t" J [I , . IE398 Final Exam Name: ?ruf. 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. TI\t~~cL ~'1'4 ~ob~ 'fjt:: = t ~((o~ ()~ +t pe j&c' ~r ,dO ~ tMtt d~eI...J ,*, t ET . S J "'1:? sl,,t' ~~A c.. r , r ~ i:~f:G ~ 0.( C~'t~~ CST ~ r ..J ~ ~, 1\ ?:6tUcC ~ '):jt~~ ?rJ~ 1}/q V M'I r\ ~ L ~'t ~:t +(r. T~t + oZ j ' S J 't ) ~J j J J j~ t~, s.t. 1jl jltTj\ \fjc.. Tl"I +1jl: = jt + Tj"to \ljtC) oJ tc" \ t IJ ji:; T Sji:: djt \fJcC) I/t:(:'\ (*) "Xjt, jt( Tjtt 5jt?) If J c ) IJ tfi:'\ , 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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