Max z = 90x_1 + 84x_2 + 70x_3 + 60x_4 s.t. 10x_1 + 8x_2 + 9x_3 + 15x_4 lessthano

Question

Max z = 90x_1 + 84x_2 + 70x_3 + 60x_4 s.t. 10x_1 + 8x_2 + 9x_3 + 15x_4 lessthanorequalto 5000 2x_1 + 3x_2 + 3x_3 + 0x_4 lessthanorequalto 1800 1x_1 + 1x_2 + 1x_3 + 1x_4 = 600 0x_1 + 0x_2 + 1x_3 + 0x_4 greaterthanorequalto 150 x_1, x_2, x_3, x_4 greaterthanorequalto 0 Use Computer Output 4. Suppose the right hand side of constraint 4 increases by 25. Which one of the following statements is guaranteed to be true? the dual price of -17 is no longer valid the problem needs to be resolved the z-value becomes 48, 025 the z-value becomes 48, 875

Explanation / Answer

Optimal Solution: z = 48025; x 1= 12.5, x2 = 412.5, x3 = 175, x4 = 0

We have use software to get this results. As the result option 3 is correct.

Table #1
==========================================================
x y z w s1 s2 s3 s4 s5 p   
==========================================================
10 8 9 15 1 0 0 0 0 0 5000   
2 3 3 0 0 1 0 0 0 0 1800   
1 1 1 1 0 0 1 0 0 0 600
0 0 1 0 0 0 0 -1 0 0 175
1 1 1 1 0 0 0 0 -1 0 600
-90 -84 -70 -60 0 0 0 0 0 1 0

Table #2
==========================================================
x y z w s1 s2 s3 s4 s5 p   
==========================================================
10 8 0 15 1 0 0 9 0 0 3425   
2 3 0 0 0 1 0 3 0 0 1275   
1 1 0 1 0 0 1 1 0 0 425
0 0 1 0 0 0 0 -1 0 0 175
1 1 0 1 0 0 0 1 -1 0 425
-90 -84 0 -60 0 0 0 -70 0 1 12250

Table #3
==========================================================
x y z w s1 s2 s3 s4 s5 p   
==========================================================
1 0.8 0 1.5 0.1 0 0 0.9 0 0 342.5
0 1.4 0 -3 -0.2 1 0 1.2 0 0 590
0 0.2 0 -0.5 -0.1 0 1 0.1 0 0 82.5   
0 0 1 0 0 0 0 -1 0 0 175
0 0.2 0 -0.5 -0.1 0 0 0.1 -1 0 82.5   
0 -12 0 75 9 0 0 11 0 1 43075

Table #4
==========================================================
x y z w s1 s2 s3 s4 s5 p   
==========================================================
1 0 0 3.5 0.5 0 0 0.5 4 0 12.5   
0 0 0 0.5 0.5 1 0 0.5 7 0 12.5   
0 0 0 0 0 0 1 0 1 0 0
0 0 1 0 0 0 0 -1 0 0 175
0 1 0 -2.5 -0.5 0 0 0.5 -5 0 412.5
0 0 0 45 3 0 0 17 -60 1 48025

Table #5
==========================================================
x y z w s1 s2 s3 s4 s5 p   
==========================================================
1 0 0 3.5 0.5 0 -4 0.5 0 0 12.5   
0 0 0 0.5 0.5 1 -7 0.5 0 0 12.5   
0 0 0 0 0 0 1 0 1 0 0
0 0 1 0 0 0 0 -1 0 0 175
0 1 0 -2.5 -0.5 0 5 0.5 0 0 412.5
0 0 0 45 3 0 60 17 0 1 48025

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