$(30$ points$)$ Remember the WeCare Insurance Co$.$ from Midterm $1?$ Below is the integer programming model they used to determine how many of their $120$ newly$-$trained agents to assign to the Great Lakes $(71),$ Gulf Coast $($x$2),$ and West Coast $($J$3)$ regions given their budget constraints and management's emphasis on the Great Lakes region:

max

$60$x$1+80$x$2+120$x$3$

s$.$t$.$

x$1+$ x$2+$ x$3120$

$55$x$1+5022+75$x$36500$

$10$x$1+25$x$2+40$x$32200$

$-07$x$1+0\mathrm{.}322+0\mathrm{.}3$x$30$

Monthly Income $($$$1000$s$)$

Available Agents

Monthly Payouts Budget $($$$1000$s$)$

Relocation Budget $($$$1000$s$)$

At Least $30\%$ of Agents to GL

X$1,22,$ x$30$ and integers

$($a$)(20)$ Convert the linear programming model above into a goal programming model that seeks to accomplish the $4$ goals below, listed from highest priority to lowest:

$$They would like a total monthly income of at least $89\mathrm{.}1$ million.

$$Since relocation expenses can be used as a tax write$-$off, they would like none of their $$2\mathrm{.}2$ million budget to be left over once new agents have been assigned.

$$They would like exactly $30\%$ of assigned agents to be sent to the Great Lakes.

$$They have decided that exceeding their relocation budget is fine as long as they don't go more than $$400,000$ over budget.

Constraints in the original model that don't directly relate to these goals should be copied into your new model without any modifications. Write this new model below.