Minimize P 6x 8y 20pts Subject to 40x 10y 2400 10x 15y 2

Minimize: P = 6x + 8y (20pts)

Subject to:

40x + 10y 2400

10x + 15y 2100

5x + 15y 1500

x 0; y 0

Solution

The given Linear Programming Problem is

Minimize: P = 6x + 8y

Subject to:

40x + 10y 2400

10x + 15y 2100

5x + 15y 1500

x 0; y 0

Using Simplex Method, we get,

Tableau #1
x y s1 s2 s3 -p
40 10 -1 0 0 0 2400   
10 15 0 -1 0 0 2100   
5 15 0 0 -1 0 1500   
6 8 0 0 0 1 0

Tableau #2
x y s1 s2 s3 -p
1 0.25 -0.025 0 0 0 60   
0 12.5 0.25 -1 0 0 1500   
0 13.75 0.125 0 -1 0 1200   
0 6.5 0.15 0 0 1 -360   

Tableau #3
x y s1 s2 s3 -p
1 0 -0.0272727 0 0.0181818 0 38.1818
0 0 0.136364 -1 0.909091 0 409.091
0 1 0.00909091 0 -0.0727273 0 87.2727
0 0 0.0909091 0 0.472727 1 -927.273   

Tableau #4
x y s1 s2 s3 -p
1 0 -0.03 0.02 0 0 30   
0 0 0.15 -1.1 1 0 450
0 1 0.02 -0.08 0 0 120
0 0 0.02 0.52 0 1 -1140

Optimal Solution : x = 30, y = 120

Minimum P = 6x + 8y= 6(30)+8(120) =180+960 = 1140

Minimum P = 1140

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