$(20$ points$)$ FlexSteal, marketed as a miracle brush$-$on sealant and baldness cure, is manufactured at three plants that are struggling to keep up with the demand at the four regional centers. The cost to ship a truckload from each of the existing plants to the regional centers is shown in the table. Note that the capacity and the total demand are both measured in truckloads.

$\backslash$table$[[,$Philadelphia,Atlanta,Dallas,Los Angeles,Capacity$],[$Plant $1,89,75,93,115,400],[$Plant $2,120,88,103,93,400],[$Plant $3,95,82,112,98,400],[$Total Demand,$350,350,350,350,]]$

The supply chain manager has explored plant construction costs in two other cities as well as the cost to ship a truckload from each of the plants to the regional centers. The current plan is to build another plant with a capacity of $400$ to allow room for sales growth. The construction cost for the new plants and cost to ship to each of the regional centers is shown here.

$\backslash$table$[[,$Philadelphia,Atlanta,Dallas,Los Angeles,Cost to Build$],[$Plant A$,94,78,95,95,$$$23,500$

$(20$ points$)$ FlexSteal, marketed as a miracle brush$-$on sealant and baldness cure, is manufactured at three plants that are struggling to keep up with the demand at the four regional centers. The cost to ship a truckload from each of the existing plants to the regional centers is shown in the table. Note that the capacity and the total demand are both measured in truckloads.

$\backslash$table$[[,$Philadelphia,Atlanta,Dallas,Los Angeles,Capacity$],[$Plant $1,89,75,93,115,400],[$Plant $2,120,88,103,93,400],[$Plant $3,95,82,112,98,400],[$Total Demand,$350,350,350,350,]]$

The supply chain manager has explored plant construction costs in two other cities as well as the cost to ship a truckload from each of the plants to the regional centers. The current plan is to build another plant with a capacity of $400$ to allow room for sales growth. The construction cost for the new plants and cost to ship to each of the regional centers is shown here.

$\backslash$table$[[,$Philadelphia,Atlanta,Dallas,Los Angeles,Cost to Build$],[$Plant A$,94,78,95,95,$$$23,500$