Explanation Given: Minimize C = 40 x + 30 y + 11 z Subject to 2 x + y + z ≥ 8 x + y − z ≥ 6 x ≥ 0 y ≥ 0 z ≥ 0 Calculation: Minimize C = 40 x + 30 y + 11 z Subject to 2 x + y + z ≥ 8 x + y − z ≥ 6 x ≥ 0 y ≥ 0 z ≥ 0 Write the tableau for the given primal problem. x y z Constant 2 1 1 8 1 1 − 1 6 40 30 11 Interchange the columns and rows of the foregoing tableau and interchange the value of x and y with the two variables u and v , obtaining the following tableau. u v Constant 2 1 40 1 1 30 1 − 1 11 8 6 Interpreting the last tableau as if it were part of the initial simplex tableau for a standard maximization problem with the exception that the signs of the coefficients pertaining to the objective function are not reversed to obtain the required dual problem as follows: Maximize P = 8 u + 6 v Subject to 2 u + v ≤ 40 u + v ≤ 30 u − v ≤ 11 u ≥ 0 v ≥ 0 The initial simplex tableau is, u v x y z p Constant 2 1 1 0 0 0 40 1 1 0 1 0 0 30 ( 1 ) − 1 0 0 1 0 11 − 8 ↑ − 6 0 0 0 1 0 Further solve the above equation. u v x y z p Constant R 1 − 2 R 3 0 ( 3 ) 1 0 − 2 0 18 R 2 − R 3 0 2 0 1 − 1 0 19 1 − 1 0 0 1 0 11 R 4 + 8 R 3 0 − 14 ↑ 0 0 8 1 88 Further solve the above equation. u v x y z p Constant 1 3 R 1 0 ( 1 ) 1 3 0 − 2 3 0 6 0 2 0 1 − 1 0 19 1 − 1 0 0 1 0 11 0 14 0 0 8 1 88 Further solve the above equation

WebAssign Printed Access Card for Tan's Finite Mathematics for the Managerial, Life, and Social Sciences, 12th Edition, Single-Term

12th Edition

ISBN: 9781337652766

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 4.2, Problem 16E

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The dual problem associated with the primal problem and the solution for the primal problem.

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Chapter 4.2, Problem 15E

Chapter 4.2, Problem 17E

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

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WebAssign Printed Access Card for Tan's Finite Mathematics for the Managerial, Life, and Social Sciences, 12th Edition, Single-Term

Ch. 4.1 - Give the three characteristics of a standard...Ch. 4.1 - a. When the initial simplex tableau is set up, how...Ch. 4.1 - In the simplex method, how is a pivoted column...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - Prob. 6E Ch. 4.1 - In Exercises 7-16, determine whether the given...

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The dual problem associated with the primal problem and the solution for the primal problem.

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