Solve the linear programming problem using the simplex method. Maximize M = x + 3y +7z...

 

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Solve the linear programming problem using the simplex method. Maximize M = x + 3y +7z subject to Find the solution. x=y=z= M = x + 4z ≤ 20 3y + z≤ 27 x. y. Z20 The Simplex Method for Problems in Standard Form 1. Introduce slack variables and state the problem in terms of a system of linear equations. 2. Construct the simplex tableau corresponding to the system. 3. Determine if the left part of the bottom row contains negative entries. If none are present, the solution corresponding to the tableau yields a maximum and the problem is solved. 4. If the left part of the bottom row contains negative entries, construct a new simplex tableau. (a) Choose the pivot column by inspecting the entries of the last row of the current tableau, excluding the right-hand entry. The pivot column is the one containing the most negative of these entries. (b) Choose the pivot element by computing ratios associated with the positive entries of the pivot column. The pivot element is the one corresponding to the smallest nonnegative ratio. (c) Construct the new simplex tableau by pivoting around the selected element. 5. Return to step 3. Steps 3 and 4 are repeated as many times as necessary to find a maximum. Solve the linear programming problem using the simplex method. Maximize M = x + 3y +7z subject to Find the solution. x=y=z= M = x + 4z ≤ 20 3y + z≤ 27 x. y. Z20 The Simplex Method for Problems in Standard Form 1. Introduce slack variables and state the problem in terms of a system of linear equations. 2. Construct the simplex tableau corresponding to the system. 3. Determine if the left part of the bottom row contains negative entries. If none are present, the solution corresponding to the tableau yields a maximum and the problem is solved. 4. If the left part of the bottom row contains negative entries, construct a new simplex tableau. (a) Choose the pivot column by inspecting the entries of the last row of the current tableau, excluding the right-hand entry. The pivot column is the one containing the most negative of these entries. (b) Choose the pivot element by computing ratios associated with the positive entries of the pivot column. The pivot element is the one corresponding to the smallest nonnegative ratio. (c) Construct the new simplex tableau by pivoting around the selected element. 5. Return to step 3. Steps 3 and 4 are repeated as many times as necessary to find a maximum.

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