Hatch Financial, which recently absorbed another firm, is now downsizing $($cutting employees$)$ and must relocate $5$ information systems analysts from recently closed locations. Yet, with the cutback, there are only $3$ jobs available. Salaries don$$t differ too much across the group. As such, moving expenses will be used as the means of determining who will be sent where and who leaves the company. Estimated moving costs for the analysts are below. Model this as an integer optimization model to minimize cost $$ indicate which $3$ analysts are kept and which location each goes to$.$

Moving Cost To

Analyst Gary Salt Lake City Fresno

Arlene $$8,500\mathrm{.}00$ $$6,000\mathrm{.}00$ $$5,000\mathrm{.}00$

Bobby $$5,000\mathrm{.}00$ $$8,000\mathrm{.}00$ $$12,000\mathrm{.}00$

Charlene $$9,500\mathrm{.}00$ $$14,000\mathrm{.}00$ $$17,000\mathrm{.}00$

Douglas $$4,000\mathrm{.}00$ $$8,000\mathrm{.}00$ $$13,000\mathrm{.}00$

Emory $$7,000\mathrm{.}00$ $$3,500\mathrm{.}00$ $$4,500\mathrm{.}00$