1. An-Najah N. University Faculty of Engineering and Information Technology Department of Management Information systems Operations Research and Applications MIS:10676213 Prepared by Mr.Maher Abubaker Fall 2015/2016 Resources Daniel J. Epstein Department of Industrial and Systems Engineering University of Southern California Andrew and Erna Viterbi School of Engineering http://www.eecs.qmul.ac.uk/~eniale/teaching/ise330/index.html Operations Research: An Introduction, 9/EHamdy A. Taha, University of ArkansasISBN-10: 013255593X ISBN-13: 9780132555937©2011 Prentice Hall Cloth, 832 ppPublished 08/29/2010 http://www.pearsonhighered.com/educator/product/Operations-Research-An- Introduction/9780132555937.page#downlaoddiv ™ INFORMS – www.informs.org ™ ORMS - www.lionhrtpub.com/ORMS.shtml ™ Science of Better - www.scienceofbetter.org

2. Chapter 2 Using Excel’s Solver to Solve Linear Programming (LP)

3. Each cell has a reference or an address, the active cell is c4

4. The selected area has the range of F3:G5, the address of the left upper corner and the right lower corner.

5. Setting up the Wyndor Glass Co. Example in an Excel Sheet

12. The following formulas should be used : Hours Used ( inside D5 cell )  =B5*B10 + C5*C10 Or =SUMPRODUCT( B5:C5;B10:C10) Because we want to drag the formula to the lower two cells ( D6 and D7 ) we use Hours Used ( inside D5 cell )  =B5*B$10 + C5*C$10 / =SUMPRODUCT( B5:C5;B$10:C$10) Total profit will be ( F10 )  =SUMPRODUCT( B2:C2;B$10:C$10)

13. After setting up the problem on the Excel Sheet Choose Solver from the Data Menu  Solver Parameter Window will displayed Fill the Parameters ( Set Target Cell, Equal To, By Changing Cells and the Constraints)

14. 1.Set Target Cell to the Total Profit ( $F$10 ) 2.Set Equal To MaX Because it is a maximization problem 3.Set the By Changing Cells to ( $B10:$C10 ) the value of the decision variables 4.Click the Add Button to add constraints

15. After Clicking the Add Button the Add Constrains Window will displayed

16. Add the first constraints which is the non-negativity constraints The changing cells ( B10:C10 ) which are the decision variables must be >= 0

17. Click Add again to add new constraints

18. The second constraint is let the values from D4:D6 <= the values from F4:F6 i.e : the Left Hand Side must be <= the Right Hand Side Then Click Ok

19. Now you are ready to solve the problem Click Solve

20. The Solver Result will displayed on the Excel Sheet Here The optimal Solution will be 2 batches of product 1 and 6 batches of product 2 The optimal total profit will be $36,000. See the video, An-Najah N. University e-learning tool on Zajel ( Moodle, Operations Research and Applications, Mr. Maher AbuBaker )