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Unformatted text preview: UF-ESI-6314b20329e767fc801a117717a3119d04f26ea48ddf.xls Problem Statementpage 1 of 9Luther Setzer1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435FoodPricePizza113$10.00 Cheese Sticks21$6.00 Calzones211$8.00 (dough)(sauce)(cheese)Another DMOR Sensitivity Analysis Example10/02/07My family owns an Italian restaurant, even though they only know how to make three Italian dishes: pizza, cheese sticks, and calzones. They would like to determine how much of each food product to make.Each food consists of dough, sauce, and cheese. We have 20 units of dough, 10 units of sauce, and 40 units of cheese available to us. Consider the following grid of resource utilization by each food, and price for which they can sell the food.DoughConsumptionSauceConsumptionCheeseConsumptionWe can thus model this problem as the following linear program, where x1is the amount of pizza produced, x2is the amount of cheese sticks produced, and x3is the amount of calzones produced:Maximize z= 10x1+ 6x2+ 8x3subject tox1+ 2x2+ 2x320x1+ x3 103x1+ x2+ x3 40x UF-ESI-6314b20329e767fc801a117717a3119d04f26ea48ddf.xls Standard Formpage 2 of 9Luther Setzer1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435Begin by recasting these equations into standard form.maximize:subject to:After optimizing this problem, we have the following optimal simplex tableau.BasicszRHSz1.00.00.05.03.07.00.0 130.00.00.01.00.50.5-0.50.05.00.01.00.01.00.01.00.010.00.00.00.0-2.5-0.5-2.51.05.0Check the optimal tableau using standard simplex tool.Maximize z = 10x1+6x2+8x3 subject tox1+2x2+2x3 <= 20x1+x3 <= 103x1+x2+x3 <= 40Optimal Solution: z = 130; x1 = 10, x2 = 5, x3 = 001z- 10x1- 06x2- 08x3= 0.0000z+ 01x1+ 02x2+ 02x3+ 01s1+ 00s2+ 00s3 = 2000z + 01x1+ 00x2+ 01x3+ 00s1+ 01s2+ 00s3= 1000z + 03x1+ 01x2+ 01x3+ 00s1+ 00s2+ 01s3= 40x 0x1x2x3s1s2s3x2x1s3http://people.hofstra.edu/Stefan_waner/RealWorld/simplex.htmlUF-ESI-6314...
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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.
- Fall '09