math125-lecture 1.5 - Sec 1.5 Thursday, February 04, 2010...

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1. Assign variables (detail and with units) 2. Define the objective function (what one is trying to optimize) 3. Define the constraints (the system of inequalities) 4. Solve the linear program Sec 1.5 Thursday, February 04, 2010 9:44 PM Section1dot5 Page 1
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1. Assign variables (detail and with units) 2. Define the objective function (what one is trying to optimize) 3. Define the constraints (the system of inequalities) 4. Solve the linear program 1. Let x = the number of days running mine 1 y = the number of days running mine 2 1.5.1 Thursday, February 04, 2010 9:44 PM Section1dot5 Page 2
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1. Assign variables (detail and with units) 2. Define the objective function (what one is trying to optimize) 3. Define the constraints (the system of inequalities) 4. Solve the linear program 1. Let x = the number of days running mine 1 y = the number of days running mine 2 2. Minimize cost: C = 2200 x + 2600 y 1.5.2 Thursday, February 04, 2010 9:44 PM Section1dot5 Page 3
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1. Assign variables (detail and with units) 2. Define the objective function (what one is trying to optimize) 3. Define the constraints (the system of inequalities) 4. Solve the linear program 1. Let x = the number of days running mine 1 y = the number of days running mine 2 2. Minimize cost: C = 2200 x + 2600 y 3. Rubies: 15 x + 10 y ≥ 150 Emeralds: 5 x + 10 y ≥ 100 Deadlines: x ≤ 25, y ≤ 25, x ≥ 0, y ≥ 0 1.5.3 Thursday, February 04, 2010 9:44 PM Section1dot5 Page 4
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1. Assign variables (detail and with units) 2. Define the objective function (what one is trying to optimize) 3. Define the constraints (the system of inequalities) 4. Solve the linear program 1. Let x = the number of days running mine 1 y = the number of days running mine 2 2. Minimize cost: C = 2200 x + 2600 y 3. Rubies: 15 x + 10 y ≥ 150 Emeralds: 5 x + 10 y ≥ 100 Deadlines: x ≤ 25, y ≤ 25, x ≥ 0, y ≥ 0 minimize C = 2200 x + 2600 y subject to 15 x + 10 y ≥ 150 5 x + 10 y ≥ 100 0 ≤ x ≤ 25 0 ≤ y ≤ 25 4. The linear program: 1.5.4 Thursday, February 04, 2010 9:44 PM Section1dot5 Page 5
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Solving the linear program Step 1: graph the constraints Rubies: 15 x + 10 y = 150 intercepts (0, 15) and (10, 0) test point (0, 0) so 0 + 0 ≥ 150 NO! Emeralds: 5 x + 10 y = 100 intercepts (0, 10) and (20, 0) testpoint (0, 0) so 0 + 0 ≥ 100 NO! Deadlines: 0 ≤ x ≤ 25, 0 ≤ y ≤ 25 1.5.5 Thursday, February 04, 2010 9:49 PM Section1dot5 Page 6
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Solving the linear program Step 1: graph the constraints Rubies: 15 x + 10 y = 150 intercepts (0, 15) and (10, 0) test point (0, 0) so 0 + 0 ≥ 150 NO! Emeralds:
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This note was uploaded on 06/07/2011 for the course MATH 125 taught by Professor Tom during the Fall '07 term at University of Illinois at Urbana–Champaign.

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math125-lecture 1.5 - Sec 1.5 Thursday, February 04, 2010...

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