A Company owns $3$ factories, in Allentown, Belton, and Concord. The factories

produce $3$ kinds of desks office, lawyer and student. The Allentown factory

produces $10$ office desks, $20$ lawyer desks, and $21$ student desks each hour. The

Belton factory produces $13$ office, $15$ lawyer, and $20$ student desks each hour.

The Concord factory produces no office desks $10$ lawyer and $15$ student desks

each hour. The Company must fill an order of at least $500$ office, $400$ lawyer and

$800$ student desks. Because of union considerations the Allentown and Belton

factories must be open at least $60$ hours altogether. If it costs the Company $$500$

per hour to run the Allentown factory, $$700$ an hour to run the Belton factory and

$$900$ an hour to run the Concord factory, how many hours must they operate each

factory to minimize the cost? What is the minimum cost?