Consider the following setup costs that are given for multi$-$facility location problem.

Site $1$ Site $2$ Site $3$ Site $4$ Site $5$

Facility $11508011020090$

Facility $2100206020070$

Facility $39021012050170$

$01\mathrm{.}12\mathrm{.}2023$

Fall Semester

a$)$ Develop a linear programming formulation for multi$-$facility location problem based on the

following assumptions:

i$.$ At most one facility can be located at each site

ii$.$ Each facility should be located at one site

iii. No interaction exists between facilities

b$)$ Find the optimal solution for the above given problem using HUNGARIAN algorithm