A small town is trying to establish a transportation system of large and small vans. It can spend no more than $100,000 for purchasing both sizes of vehicles and no
more than $500 per month for maintenance. The town can purchase a small van for
$10,000 and maintain it for $100 per month. The large vans cost $20,000 each and
can be maintained for $75 per month. Each large van carries a maximum of 15
passengers and each small van carries a maximum of 7 passengers. Find the
maximum number of passengers the transportation system can handle given the
constraints. How many large and small vans will they need to maximize the
number of passengers it can service?