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(Solved): Problem 2: Parametric Linear Programming Consider the following problem: maximize Z(\theta )=(10-\th ...
Problem 2: Parametric Linear Programming
Consider the following problem:
maximize Z(\theta )=(10-\theta )x_(1)+(12+\theta )x_(2)+(7+2\theta )x_(3)
s.t. x_(1)+2x_(2)+2x_(3)<=30
,x_(1)+x_(2)+x_(3)<=20
,x_(1),x_(2),x_(3)>=0.
(a) Use parametric linear programming to find an optimal solution for this problem as a
function of \theta , for \theta >=0.
(b) Write the associated dual problem. Then, find an optimal solution for this dual problem
as a function of \theta , for \theta >=0. Compare the basic solutions obtained with the comple-
mentary basic solutions obtained in part (a).