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Excel Session 2 - ARE 155 Fall 1999 Richard Howitt Excel...

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ARE 155 Fall 1999 Excel Session #2 Richard Howitt Getting Started with the Solver Now we will begin to use Excel to solve linear programming problems. When there are more than two decision variables, we’re no longer able to solve LP problems graphically the way we’ve been doing. Besides adopting linear algebra techniques, we have to resort to computing to find the solution. It’s very easy and intuitive to do so with the Excel Solver, as we shall now demonstrate. Let’s start off with the simple linear program Max ( z = 5 x 1 + 2 x 2 + 8 x 3 ) s . t . x 1 2 x 2 + 0.5 x 3 420 2 x 1 + 3 x 2 x 3 610 6 x 1 x 2 + 3 x 3 125 x 1 , x 2 , x 3 0 We can write it out on the spreadsheet, using formulas to define the objective function and constraints, as shown below: Notice that we’ve left the decision variable cells blank – this is very important . Excel will fill those cells with the optimal values, so we can leave them at zero (as if we’re starting at the origin of the feasible region). Also notice that we’ve written the objective function value and the LHS of the constraints as
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ARE 155 Fall 1999 2 Excel Session #2 formulas. That way Excel can always keep track of their values when it’s looking for the optimal solution, and ensure that the final solution is both feasible and optimal. Once we’ve written out the mathematical program in a way that Excel can understand, we can go ahead and launch the Solver from the Tools menu, as shown below: When we get the dialog box for the Solver, we make sure that the “Target Cell” address is the correct one for the objective function value (I recommend clicking on this cell before launching Solver so that it automatically is set). We make sure that the “M ax” button is checked (given our problem), and that the
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