$(2)$ Wayfair purchases sofas from $2$ warehouses located in Georgia. The sofas purchased at each of these locations during the current cycle is as follows Norcross :$950$ Atlanta: $875$ Wayfair sells these sofas at $3$ outlets in Georgia and South Carolina. The expected sales in the current cycle at each of these outlets is as follows$+$ Greenville: $325$ Columbia: $695$ Savannah: $550$ The cost of transporting sofas from one location to the next is given below Greenville Columbia Savannah Norcross $181628$ Atlanta $725066$ Greenville NA $2523$ Columbia $29$ NA $31$ Savannah $2029$ NA Formulate a model that minimizes total transportation costs