Introduction to Optimization
MS&E 111/ENGR 62, Fall 2013-2014, Stanford University
Instructor: Ashish Goel
Homework 6. Given 11/22/13. Due 12/04/13 at 6:00PM (at the Huang HW Cabinet)
Provide numerical examples (objective function and constraints) for each of the following cases.
Say whether the primal and dual are unbounded and whether each has an optimal solution.
(a) Primal feasible, dual feasible.
(Example answer: Both primal and dual have optimal solutions.
optimal primal solution = optimal dual solution).
(b) Primal feasible, dual infeasible.
(c) Primal infeasible, dual feasible.
(d) Primal infeasible, dual infeasible.
ARC Consultants need to know how long it will take to complete a particular job. The job
different tasks. Each task
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
where the (
)th element of the matrix is a 1 if task
must be performed
and a 0 otherwise. (Note that all elements on the diagonal must be zero as a task cannot be