$[$Formulation Only$][5$ points$]$ The West Hartford Senior Center is trying to establish a transportation system of small and large vans. It can spend no more than $$100,000$ for both sizes of vehicles and no more than $$500$ per month for maintenance. The WHSC can purchase a small van, which carries up to $7$ passengers, for $$10,000$ and maintain it for $$100$ per month. The large vans, which carry up to $15$ passengers, cost $$20,000$ each and can be maintained for $$75$ per month. How many of each type of van should they purchase if they want to maximize the number of