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Cách sử dụng hàm Solver trong Excel, ứng dụng vào tính toán trong môn Quy hoạch tuyến tính
Linear Programming Using Excel Subject: Linear Programming using Excel Application: Microsoft Excel 2007 Task: Solving a Linear Program Using Excel Install the Solver Add-In 1. In the Microsoft Office button, go to excel options to click Add-ins 2. In the Add-Ins box, select Solver Add-In and click Go Install the Solver Add-In (continue) 3. In the Add-Ins available box, check the Analysis ToolPak and then OK 4.2 Exercises 307 To initiate the program, select PRGM <SMPLX> ENTER , and you will see the screens Enter the first pivot column, column 1 and ENTER , to obtain the screens The ratios 240 and 150 indicate the second row is the pivot row. Press ENTER and enter 2. Press ENTER to obtain the next tableau. A B C D 1 2 3 4 5 6 Using Excel Using Solver Excel has a program, Solver, that does the computations for a linear programming problem. We use the follow- ing example to illustrate how it is used. Maximize z 5 5x 1 1 8x 2 1 7x 3 subject to 3x 1 1 2x 2 1 x 3 Յ 660 x 1 1 4x 2 1 2x 3 Յ 740 2x 1 1 x 2 1 3x 3 Յ 853 x 1 Ն 0, x 2 Ն 0, x 3 Ն 0 Here’s how we set up the problem. We use the cells A1:C1 for the values of the variables x 1 , x 2 , and x 3 . Solver will adjust the values of the variables until the objective function reaches the optimal value. We begin by entering x 1 5 0 in A1, x 2 5 0 in B1, and x 3 5 0 in C1. Next we enter the formulas for the left side of the constraints, the nonnegative conditions and the objective function in column D, and the number on the right side in column E. Unless otherwise noted, all content on this page is © Cengage Learning. Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 308 Chapter 4 Linear Programming: The Simplex Method To start up Solver, click on the Data tab. Move to the Analysis group and click on Solver. • PlacethecursorintheboxnexttoSet Target Cell, or Set Objective, depending on your version of Excel. • SelectcellD7, since this is the location of the formula for the objective function. • Checkthebuttontomaximize, since this is a maximization problem. Excel 2007 Excel 2010 Place the cursor in the box under By changing cells: and then select cells A1:C1 (the cells containing the variables). Excel 2007 Excel 2010 You are now ready to enter the constraints. Move the cursor to the box under Subject to the Constraints: and click on the button shown as Add to obtain Make sure the cursor is in the box under Cell Reference: and select cell D1; then move the cursor to the box under Constraint: and select the cell E1. Click the Add button. Repeat the preceding step using cells D2 and E2, then D3 and E3. Click Ok. You have entered the constraints. Note that the constraints have the symbol ,5 between Cell Reference: and Constraint: (this represents #). Excel 2007 Excel 2010 Unless otherwise noted, all content on this page is © Cengage Learning. Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 4.2 Exercises 309 Click on the Add button to enter the nonnegative conditions. Again place the cursor in the Cell Reference: box and select cell D4. Then select E4 for the Constraint: box. Since this is a nonnegative condition, we need the $ symbol; get it by selecting .5. Then click Add. In the same way, enter the nonnegative constraints using D5, E5 and D6, E6. You will then have the screen Excel 2007 Excel 2010 Now set the options for Solver, depending on your version. Excel 2007 Excel 2010 Click into the Options box, and make sure Make sure the Simplex LP method is selected in the that the Assume Linear Model checkbox is dialog box. checked, as in the following figure. Leave all other options as is, and click Ok. Click on the Solve button to obtain the solution. The maximum value of z 5 2386 at (116, 63, 186). Unless otherwise noted, all content on this page is © Cengage Learning. Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. . then have the screen Excel 2007 Excel 2010 Now set the options for Solver, depending on your version. Excel 2007 Excel 2010 Click into the Options box, and make sure Make sure the Simplex LP. Excel Subject: Linear Programming using Excel Application: Microsoft Excel 2007 Task: Solving a Linear Program Using Excel Install the Solver Add-In 1. In the Microsoft Office button, go to excel. variables). Excel 2007 Excel 2010 You are now ready to enter the constraints. Move the cursor to the box under Subject to the Constraints: and click on the button shown as Add to obtain Make sure