DMOR-04-03 - UF-ESI-6314DMOR-04-03 Problem Statementpage 1 of Hot DogsBad-for- z= 7c 0i 3g 10b 8hsubject toI am trying to figure out how to fill up

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Unformatted text preview: UF-ESI-6314DMOR-04-03.xls Problem Statementpage 1 of 9ItemsChipsIceGatoradeBeer Hot DogsBad-for-you1552515Preference73108Maximize z= 7c+0i+3g+10b+8hsubject toI am trying to figure out how to fill up my cooler for this weekend's tailgating party. I can fill it up with chips, ice, Gatorade, beer, and hot dogs. Let's measure the amount of each item that I put in the cooler by the % space of the cooler that it fills. I have to keep the Gatorade, beer, and hot dogs cold, so I need at least as much ice in the cooler as I have these three items. I'm going to get thirsty while I'm there, so I need to have at least 50% of the cooler filled with items that I can drink (ice counts as an item that I can drink, since it will melt).The "bad-for-you" value of each item, and my preference for each item, is given in the following table. I will put a hard constraint that I cannot have more than 10 total units of "bad-for-you" items in my cooler.Associate variables c, i, g, b, and hwith these products (that's the percentage of space that each of these items takes up in my cooler). Hence, my optimization problem is formulated as follows.Questions 3 through 9 (5 points each). Now, the remaining questions are related to sensitivity analysis. Consider the following example.I will put a hard constraint that I cannot have more than 10 total units of "bad-for-you" items in my cooler. Add a slack variable s1.I can fill it up with chips, ice, Gatorade, beer, and hot dogs. Let's measure the amount of each item that I put in the cooler by the % space of the cooler that it fills. Add a slack variable s2.I have to keep the Gatorade, beer, and hot dogs cold, so I need at least as much ice in the cooler as I have these three items. Subtract a slack variable s3.I'm going to get thirsty while I'm there, so I need to have at least 50% of the cooler filled with items that I can drink (ice counts as an item that I can drink, since it will melt). Subtract a slack variable s4.c, i, g, b, h≥15c+0i+5g+25b+15h≤101c+1i+1g+1b+1h≤1c+1i-1g-1b-1h≥c+1i+1g+1b+0h≥0.5Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435UF-ESI-6314DMOR-04-03.xls Standard Formpage 2 of 9maximize:01z- 07c- 00i- 03g- 10b- 08h= 00.0subject to:00z + 15c+ 00i+ 05g+ 25b+ 15h+ 01s1+ 00s2+ 00s3+ 00s4= 10.000z + 01c+ 01i+ 01g+ 01b+ 01h+ 00s1+ 01s2+ 00s3+ 00s4= 01.000z + 00c+ 01i– 01g– 01b– 01h+ 00s1+ 00s2- 01s3+ 00s4= 00.000z + 00c+01i+ 01g+ 01b+ 00h + 00s1+ 00s2+ 00s3- 01s4= 00.5c, i, g, b, h≥s≥Here's the optimal tableau....
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This note was uploaded on 02/25/2010 for the course ESI 6314 taught by Professor Vladimirlboginski during the Fall '09 term at University of Florida.

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DMOR-04-03 - UF-ESI-6314DMOR-04-03 Problem Statementpage 1 of Hot DogsBad-for- z= 7c 0i 3g 10b 8hsubject toI am trying to figure out how to fill up

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