Solve the fallowing linear programming problem algebraically using the simplex m

Question

Solve the fallowing linear programming problem algebraically using the simplex method (not the tableau). At each "update" (which must be clearly shown). stale the basic feasible solution. Identify which variable which increases 'z' the most by entering the basis (if not optimal) Identify which variable leaves the basis (if not optimal) maximize z = 2x_1 + 3x_2 + x_3 subject to x_1 + x_2 + 4X_3 lessthanorequalto 100 x_1 + 2X_2 + x_3 lessthanorequalto 150 3x_1 + 2X_2 + x_3 lessthanorequalto 320 with X_1, X_2, X_3 greaterthanequalto 0 Your solution should contain the following information at the end: Maximum z = when x_1 = x_2 = x_3 =

Explanation / Answer

Tableau #1
x1 x2 x3 s1 s2 s3 p   
1 1 4 1 0 0 0 100
1 2 1 0 1 0 0 150
3 2 1 0 0 1 0 320
-2 -3 -1 0 0 0 1 0

Tableau #2
x1 x2 x3 s1 s2 s3 p   
0.5 0 3.5 1 -0.5 0 0 25   
0.5 1 0.5 0 0.5 0 0 75   
2 0 0 0 -1 1 0 170
-0.5 0 0.5 0 1.5 0 1 225

Tableau #3
x1 x2 x3 s1 s2 s3 p   
1 0 7 2 -1 0 0 50   
0 1 -3 -1 1 0 0 50   
0 0 -14 -4 1 1 0 70   
0 0 4 1 1 0 1 250

The maximum value will occur when x1=50,x2=50 and x3=0

Maximum value = 250

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