Assignment Problem 1: Consider the attached Multi-objective problem related to Control Engineering and answer the three questions below:
Q1. Set up and solve this problem with EXCEL Solver for various values (at least 3) of weighting parameter c (it is likely a small number-order of magnitude around 0.01).
Q2. Plot optimal voltage u*(k)(free) and position x1*(k) against target position k for various values of c (e.g., 3 values).
Q3. Determine best compromise solution between accuracy & control smoothness.
Assignment Problem 2: Consider the attached transportation problem and answer the questions below:
Q1. Set up and solve this problem with EXCEL Solver [Note: there is specialized transportation algorithm that uses dual to solve this problem very efficiently-but we will use Solver].
Q2. Examine the reduced costs to find current non-basic variables with 0 reduced cost. Use previous method to force entry of this variable into basis and solve again.
Q3. We are looking for solutions that minimize the total company-wide cost, but give relatively even distribution of total costs at each warehouse (since each warehouse manager is required to pay all freight costs from plants to their warehouse.
If there is too much disparity between the freight costs each manager has to pay, they will complain that it is not fair.
Select alternate solution that minimizes the variance between the total freight costs at each warehouse as compared to other solutions. This is the solution likely be implemented by the Company.
Instructions for the two problems:
A) Excel Solver must be used for solving the problems with the problem setup in Excel corresponding to the structure.
B) First formulate the objective function and all constraints. There is no need to add slack or surplus variables since Excel Solver adds them automatically, but there are free variables, include the method for dealing with free variables.
C) Insert screen shots of the Excel problem setup with the solutions clearly displayed in the screen shots.
D) Include graphical plots of the solutions where appropriate.
E) Add screen shots of the Sensitivity and Limits Reports from the Solver solutions only if needed to answer the questions for that problem.
F) The solutions must be submitted along with a single Excel *.xlsx file containing tabbed worksheets for the problem. Do not upload separate xlsx files for each question.
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Attachment:- Control Engineering.rar