The Very Possible Foods Company makes vegan versions of hamburgers, hot dogs, and chicken wings, and they offer two platters. Platter A consists of $1$ burger, $3$ hot dogs, and $5$ chicken wings, which costs $\$16.$ Platter B consists of $2$ burgers, $1$ hot dog, and $8$ chicken wings, which costs $\$20.$ A barbecue 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)?
