Simplex Method Exercise A toy store uses three operations to assemble three types of toys: trains, trucks, and cars. The daily times available for the three operations are 430, 460, and 420 minutes, respectively, and the revenue per train unit, toy truck and car are $3, $2, $5 USD. The assembly times per train in the three operations are 1, 3 and 1 minutes. The corresponding times per truck 2, 0 and 4 minutes. As for cars, they are 1, 2 and 0 minutes (a time zero indicates that the operation is not used. Let x, y, and z The daily quantities of assembled units of trains, trucks and cars, respectively, are all summarized in the following table: Variables Case: Toy store - Simplex Method The decision variables are the items that are going to be produced in this case trains, trucks and cars. x1 = trains x2 = trucks X3 = cars Objective Function The objective function of the problem is determined by income Z = INCOME MAX Z = 3X1 + 2X2 + 5X3 Restrictions Case: Toy store - Simplex Method In this case the restrictions are the operations that are subject to the time factor: R1: X1 + 2X2 +X3 ≤ 430 A2: 3X1 + 2X3 ≤ 460 A3: X1 + 4X2 ≤ 420 Algebraic Model MAX Z = 3X1 + 2X2 + 5X3 s.a 1X1 + 2X2 +1X3 ≤ 430 3X1 +0X2 + 2X3 ≤ 460 1X1 + 4X2 +0X3 ≤ 420 x1,X2,X3 ≥ 0 Toy store - Simplex Method Operations Case: Toy store - Simplex Method The Objective Function is Equated to 0 MAX Z -3X1 - 2 X 2- 5X3 = 0 The constraints should still be equal, but a Slack variable is added: 1X1 + 2X2 +1X3 +S1 = 430 3X1 +0X2 + 2X3 +S2 = 460 1X1 + 4X2 +0X3+S3 = 420 This slack variable is currently unknown. Make Simplex Tables To Complete the Exercise Obtain: ● The daily assembled units of each Toy ● Total Income ● Slack Variables

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Simplex Method Exercise A toy store uses three operations to assemble three types of toys: trains, trucks, and cars. The daily times available for the three operations are 430, 460, and 420 minutes, respectively, and the revenue per train unit, toy truck and car are $3, $2, $5 USD. The assembly times per train in the three operations are 1, 3 and 1 minutes. The corresponding times per truck 2, 0 and 4 minutes. As for cars, they are 1, 2 and 0 minutes (a time zero indicates that the operation is not used. Let x, y, and z The daily quantities of assembled units of trains, trucks and cars, respectively, are all summarized in the following table: Variables Case: Toy store - Simplex Method The decision variables are the items that are going to be produced in this case trains, trucks and cars. x1 = trains x2 = trucks X3 = cars Objective Function The objective function of the problem is determined by income Z = INCOME MAX Z = 3X1 + 2X2 + 5X3 Restrictions Case: Toy store - Simplex Method In this case the restrictions are the operations that are subject to the time factor: R1: X1 + 2X2 +X3 ≤ 430 A2: 3X1 + 2X3 ≤ 460 A3: X1 + 4X2 ≤ 420 Algebraic Model MAX Z = 3X1 + 2X2 + 5X3 s.a 1X1 + 2X2 +1X3 ≤ 430 3X1 +0X2 + 2X3 ≤ 460 1X1 + 4X2 +0X3 ≤ 420 x1,X2,X3 ≥ 0 Toy store - Simplex Method Operations Case: Toy store - Simplex Method The Objective Function is Equated to 0 MAX Z -3X1 - 2 X 2- 5X3 = 0 The constraints should still be equal, but a Slack variable is added: 1X1 + 2X2 +1X3 +S1 = 430 3X1 +0X2 + 2X3 +S2 = 460 1X1 + 4X2 +0X3+S3 = 420 This slack variable is currently unknown. Make Simplex Tables To Complete the Exercise Obtain: ● The daily assembled units of each Toy ● Total Income ● Slack Variables