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Unformatted text preview: Practice Final AEM 412 You should be able to finish your test in 2:30 minutes comfortably. Read the questions carefully. For each question read all its subquestions before starting answering it. I also suggest that you read all the questions before starting answering them so that you can decide how you want to allocate your time. I have checked and there are (not including this one), _________ pages in the final exam handout (fill in the blank). Further, in signing below I agree to abide by the Cornell University Code of Academic Integrity with respect to this exam. Name ______________________________ Email Address ____________________________ Signature_______________________________ May 18, 2005. Here is a suggestion for the allocation of your time among questions [ 100 points total]: Q1. 30 minutes ( [25 points] Linear Programming and Computer Analysis ) Q2. 15 minutes ( [25 points] Network Models I). Q3. 20 minutes ( [25 points] Network Models II) Q4. 15 minutes ( [10 points] Duality) Q5. 15 minutes ( [15 points] Integer Programming). GOOD LUCK ! 1 1. [25 points] Linear Programming and Computer Analysis Carco manufactures cars and trucks. Each car contributes $300 to profit and each truck, $400. The resources required to manufacture a car and truck are shown in the table below. Each day, Carco can rent up to 98 type 1 machines at a cost of $50 per machine. At present, the company has 73 type 2 machines and 260 tons of steel available. Marketing considerations dictate that at least 88 cars and at least 26 trucks be produced. Let X1 – number cars produce daily X2 – number of trucks produced daily M1 – type 1 machines rented daily Days on Type 1 Machine Days on Type 2 Machine Tons of steel Car 0.8 0.6 2 Truck 1 0.7 3 To maximize profit, Carco should solve the following LP (it’s okay to get fractional solutions – this is only for planning purposes). Max 300 X1 + 400 X2 – 50 M1 Subject to: 0.8 X1 + X2 – M1 <= 0; M1 <= 98; 0.6 X1 + 0.7 X2 <= 73; 2 X1 + 3 X2 <= 260; X1 >= 88; X2 >= 26; X1 >=0; X2 >=0; 2 1a) [10 points] Formulate the dual problem. Min W = 98 Y2 + 73 Y3 + 260 Y4  88 Y5  26 Y6 S.t. 0.8 Y1 + 0.6 Y3 + 2 Y4 +  Y5 >= 300; Y1 + 0.7 Y3 + 3 Y4  Y6 >= 400;Y1 + Y2 >= 50; Y 1,2,3,4,5,6 >= 0 3 Use the MPL output to answer the questions below. MPL Modeling System  Copyright (c) 19882000, Maximal Software, Inc....
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This note was uploaded on 02/25/2011 for the course AEM 4120 taught by Professor Gomes,c. during the Fall '08 term at Cornell.
 Fall '08
 GOMES,C.

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