Linear Program Problem ARC Consultants needs to know how long it will take to co

Question

Linear Program Problem

ARC Consultants needs to know how long it will take to complete a particular job. The job consists of (n) different tasks. Each task (k) takes (tk) hours to complete (regardless of how many people work on it).

Additionally, certain tasks cannot be performed until other tasks have been completed. This information is represented in a (n)x(n) matrix P where the (i, j)th element of the matrix is set to 1 if task (j) must be performed before task (i) and a 0 otherwise. (Note that all elements on the diagonal must be zero as a task cannot be performed before itself.) There is no limit on the number of tasks that can be performed at once.

Question:

Set up a linear program that determines how soon ARC can complete the job. As always, clearly specify your decision variables, objective function and constraints.

Explanation / Answer

1) objective function

Minimixe the time = tk

Decision variables = k

Constraints = n

=n+k > tk

=n+k< 0

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