1. Minimize Problems Produced by E. Gretchen Gascon

2. Concept of Duels Given ProblemDuel problem m # of variablesn # of variables n # of constantsm # of constants Coefficients from objective function ( bottom row)Constraint constants (last column) Constraint constants (left column)Coefficients from objective function ( bottom row) To solve a minimization problem by the method of duels: 1- convert the minimize problem into a maximize problem by transposing the matrix 2- Solve the maximize problem as previously 3 – Read the answer from the bottom row.

3. Problem 4.3 # 11 1- convert the minimize problem into a maximize problem by transposing the matrix The rows become the columns and the columns become the rows. Now read the transposed matrix Notice: the inequality changed direction

4. Problem 4.3 # 11 con’t 2- Solve the maximize problem as previously

5. Problem 4.3 # 11 con’t Solution Minimum value = maximum value = 40 y1 = s1 = 10 y2 = s2 = 0 3 – Read the answer from the bottom row, column s1 and s2.

6. Same Problem with EXCEL Solver 1. Start by entering the following into an Excel Spreadsheet. You can find a tutorial document in course material (week 2) on using the Solver. 2. Make cell B3 the active cell, and select the Solver (this will be different depending upon which version of Excel you have) (You may need to add in the solver if you do not already have it.) Your spread sheet should look like 

7. Solver window Be sure to check the solver options: Be sure to check Min not Max

8. Solution By Solver: By Matrix Algebra (slide # 5) The answer: y1 = 10 and y2 = 0 Read the answer from the bottom row of the matrix

9. Review Two ways were shown how to complete Minimization problems. Please post comments, questions, regarding this slide presentation in the Main forum