A bank has $4$ sites at which checks are processed. The daily capacity for these sites are: A $-6000$ checks; B $-8000$ checks; C $-7000$ checks; D $-9000$ checks. The bank processes $4$ types of checks: vendor, salary, personal and household. The processing cost per check $($in cents$)$ depends on the site and is given on the table below. Each day, $7000$ vendor checks, $6000$ salary checks, $8000$ personal checks, and $7000$ household checks need to be processed. The objective is to minimize the total daily cost of processing checks.