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Pizza - UF-ESI- Problem Statementpage 1 of 9 Another DMOR...

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UF-ESI-6314b20329e767fc801a117717a3119d04f26ea48ddf.xls Problem Statementpage 1 of 9 Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435 Food Price Pizza 1 1 3 $10.00 Cheese Sticks 2 0 1 $6.00 Calzones 2 1 1 $8.00 (dough) (sauce) (cheese) Another DMOR Sensitivity Analysis Example 10/02/07 My 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. Dough Consumption Sauce Consumption Cheese Consumption We can thus model this problem as the following linear program, where x 1 is the amount of pizza produced, x 2 is the amount of cheese sticks produced, and x 3 is the amount of calzones produced: Maximize z = 10 x 1 + 6 x 2 + 8 x 3 subject to x 1 + 2x 2 + 2 x 3 20 x 1 + x 3 ≤ 10 3 x 1 + x 2 + x 3 ≤ 40 x 0
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UF-ESI-6314 b20329e767fc801a117717a3119d04f26ea48ddf.xls Standard Form page 2 of 9 Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435 Begin by recasting these equations into standard form. maximize: subject to: After optimizing this problem, we have the following optimal simplex tableau. Basics z RHS z 1.0 0.0 0.0 5.0 3.0 7.0 0.0 130.0 0.0 0.0 1.0 0.5 0.5 -0.5 0.0 5.0 0.0 1.0 0.0 1.0 0.0 1.0 0.0 10.0 0.0 0.0 0.0 -2.5 -0.5 -2.5 1.0 5.0 Check the optimal tableau using standard simplex tool. Maximize z = 10x1+6x2+8x3 subject to x1+2x2+2x3 <= 20 x1+x3 <= 10 3x1+x2+x3 <= 40 Optimal Solution: z = 130; x1 = 10, x2 = 5, x3 = 0 01 z - 10 x 1 - 06 x 2 - 08 x 3 = 0.00 00 z + 01 x 1 + 02x 2 + 02 x 3 + 01 s 1 + 00 s 2 + 00 s 3 = 20 00z + 01 x 1 + 00 x 2 + 01 x 3 + 00 s 1 + 01 s 2 + 00 s 3 = 10 00z + 03 x 1 + 01 x 2 + 01
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