Afirm has plants in boston and baltimore that manufacture three models of hot tubs: regular, fancy, and super. in one day the boston plant can manufacture 20 of the regular model, 24 of the fancy model, and 12 of the super model, and costs $4500 per day to operate, whereas the baltimore plant can manufacture 12 of the regular model, 16 of the fancy model, and 32 of the super model, and costs $2000 per day to operate. at least 276 of the regular model, 360 of the fancy model, and 468 of the super model are needed. how many days must each plant operate in order to minimize the cost?