The Highly Improbable Foods Company makes vegetarian versions of burgers, hot dogs, and chicken wings, and they offer two platters. Platter A consists of one burger, three hot dogs, and $5$ chicken wings, which costs $\$16.$ Platter B consists of two burgers, one hot dog, and $8$ chicken wings, which costs $\$20.$

A picnic organizer requires $80$ hamburgers, $95$ hot dogs, and $380$ chicken wings. (There can be leftovers, but these are the minimum requirements.) What is the minimum cost (in dollars)?