Question: Consider the following linear program: max. Xn j=1 cjxj (1) subject to Xn j=1 aijxj bi , i = 1, . . . , m

Consider the following linear program:

max. Xn j=1 cjxj (1)

subject to Xn j=1 aijxj bi , i = 1, . . . , m xj 0, j = 1, . . . , n (2)

Formulate the dual of this program.

Change some of the constraints of the LP 1 into equalities. Show that the dual of this new program results in the corresponding dual variables being unconstrained.

Additionally, show that if some of the variables in LP 1 are unconstrained, then the corresponding constraints in the dual become equalities.

please give me detailed solutionthanks

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