State University must purchase $1200$ computers from

three vendors. Vendor $1$ charges $$250$ per computer

plus a total delivery charge of $$5000.$ Vendor $2$ charges

$$300$ per computer plus a total delivery charge of

$$4000.$ Vendor $3$ charges $$350$ per computer plus a

total delivery charge of $$6000.$ Vendor $1$ will sell the

university at most $800$ computers, vendor $2,$ at most

$600,$ and vendor $3,$ at most $400.$ The minimum order

from any vendor is $300$ computers. Determine how to

minimize the cost of purchasing the needed computers