Answered: olve the standard minimization problem…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Solve the standard minimization problem using duality. (You may already have seen some of them in earlier sections, but now you will be solving them using a different method.)

Minimize c = s + t + u subject to

3s + 2t + u ≥ 84
2s + t + 3u ≥ 84
s + 3t + 2u ≥ 84
s ≥ 0, t ≥ 0, u ≥ 0.

c=(s, t, u)

Expert Solution

Step 1

Dual Problem with Standard maximization:

1. Create a matrix with the constraints and objective function without slack variables, with the first column containing the first variable's coefficients, the second column the second variable's coefficients, and so on. Allow the final column to indicate each constraint's constant. Place a 1 in the objective function (final row) to reflect the coefficient of the objective function's name.
2. Determine the matrix's transpose.
3. The Dual Problem is when you rewrite the constraints and goal function using the new matrix. Assume that each additional column represents the coefficients of all the original variables.