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Find the optimum solution to the following LP by using the Simplex Algorithm. Min z = 3x1...

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Advance Math

Find the optimum solution to the following LP by using theSimplex Algorithm.

Min z = 3x1 – 2x2+ 3x3

s.t.
-x1 + 3x2 ≤ 3

x1 + 2x2 ≤ 6

x1, x2, x3≥ 0

a) Convert the LP into a maximization problem in standardform.

b) Construct the initial tableau and find a bfs.

c) Apply the Simplex Algorithm.

Answer & Explanation Solved by verified expert
3.8 Ratings (449 Votes)
Elements of the column basis BTransfer to the table the basic elements that we identified inthe preliminary stageB1 x4B2 x5Cb column itemsEach cell of this column is equal to the coefficient whichcorresponds to the base variable in the corresponding rowCb1 0Cb2 MValues of variable variables and column PAt this stage no calculations are needed just transfer thevalues from the preliminary stage to the corresponding tablecellsP1 3P2 6x11 1x12 3x13 0x14 1x15 0x21 1x22 2x23 0x24 0x25 1Objective function valueWe calculate the value of the objective function by elementwisemultiplying the column Cb by the column P adding the results ofthe productsMinP Cb1 P01 Cb11 P2 0 3 M 6 6MEvaluated Control VariablesWe calculate the estimates for each controlled variable byelementwise multiplying the value from the variable column by thevalue from the Cb column summing up the results of the productsand subtracting the coefficient of the objective function fromtheir sum with this variableMinx1 Cb1 x11 Cb2 x21 kx1 0 1 M 1 3 M3Minx2 Cb1 x12 Cb2 x22 kx2 0 3 M 2 2 2M2Minx3 Cb1 x13 Cb2 x23 kx3 0 0 M 0 3 3Minx4 Cb1 x14 Cb2 x24 kx4 0 1 M 0 0 0Minx5 Cb1 x15 Cb2 x25 kx5 0 0 M 1 M 0Q column itemsSince there are positive values among the estimates of thecontrolled variables the current table does not yet have anoptimal solution Therefore in the basis we introduce the variablewith the highest positive estimateThe number of variables    See Answer
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