PLEASE SOLVE THIS WITHOUT EXCEL STEP BY STEP INDUSTRIAL ENGINEERING Maximize z =

Question

PLEASE SOLVE THIS WITHOUT EXCEL

STEP BY STEP

INDUSTRIAL ENGINEERING

Maximize z = 2x1 +3x2 +x3 +4x4 Subject to x1 x3 + x4 5 x1 +2x2 +x4 6 x2 +2x3 +0.5x4 8 xj0,j=...1, ,4 (a) Write the canonical form (or simplex form) of the LP model (call this iteration 0). (b) Perform two iterations (call these iterations 1 and 2) of the simplex algorithm. (c) What is the basic feasible solution you get from your last iteration (iteration 2)? Clarify basic variables and nonbasic variables. Also give the values of all the variables and the objective function. (d) Is the basic feasible solution you get from your last iteration (iteration 2) optimal? Why or why not?

Explanation / Answer

Maximize-Z=2X1+3X2+X3+4X4+0S1+0S2+0S3

subject to constraint X1-X3+X4+S1=5

-X1+2X2+X4+S2=6

X2+2X3+0.5X4+S3=8

X1, X2, X3, X4>=0

Prepare a table like this and find the ratio until for a maximization problem CJ-Zj<=0

Max value of Cj-Zj in the table below is 4, selecting the column and calculating the ratio based on values of X4

Iteration 0 CBi Cj 2 3 1 4 0 0 0 BV X1 X2 X3 X4 S1 S2 S3 Solution Ratio 0 S1 1 0 -1 1 1 0 0 5 5/1=5 0 S2 -1 2 0 1 0 1 0 6 6/1=6 0 S3 0 1 2 0.5 0 0 1 8 8/0.5=16 Zj 0 0 0 0 0 0 0 Cj-Zj 2 3 1 4 0 0 0 Iteration 1 CBi Cj 2 3 1 4 0 0 0 BV X1 X2 X3 X4 S1 S2 S3 Solution Ratio 1 X4 1 0 -1 1 1 0 0 5 0 S2 0 2 -1 2 1 1 0 11 0 S3 0 1 2 0.5 0 0 1 8 Zj 1 0 -1 1 1 0 0 Cj-Zj 1 3 2 3 -1 0 0 0 X4 column now becomes the key column

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