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1. Consider the following standard production problem
Maximize c'x
s.t. Ax <= b
Xi >= 0
Where A is an m by n matrix (m constraints and n variables), x is an n by 1 vector, and b
is an m by 1 vector. A' is the transpose matrix of A.
Its dual problem is
Minimize b'y
s.t. A'y c
Yi >= 0
For the given primal problem below, write out the dual problem in the table.
PRIMAL
Maximize
3x1+5x2
Subjected to x1<= 4 (resource 1)
2x2< 12 (resource 2)
3x1+2x2<=18 (resource 3)
X1,
X2 >= 0
DUAL

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