1) Consider the following Linear Programming problem: Maximize Z = 5 X1 + 8 X2 Subject to: 8 X1 + 15 X2 <= 6,300 4 X1 +

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1) Consider the following Linear Programming problem:
Maximize Z = 5 X1 + 8 X2
Subject to:
8 X1 + 15 X2 <= 6,300
4 X1 + 2 X2 <= 1,800
15 X1 + 30 X2 <= 12,000
X1 and X2 real and positive.
Which with slack variables is as:
Maximize Z = 5 X1 + 8 X2 + 0 X3 + 0 X4 + 0 X5
Subject to:
8 X1 + 15 X2 + X3 = 6,300
4 X1 + 2 X2 + X4 = 1,800
15 X1 + 30 X2 + X5 = 12,000
All real and positive variables.
a) State the dual problem of the previous problem, expressing it in
canonical and complete form.
b) What are the optimal values ​​of the dual problem? (All
variables)
c) What variables would be at the base of the optimal solution
if the first constraint of the problem changed to 8 X1 + 15 X2 + X3
= 6,000?