Problem 2: 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. 2 1 L Site (cents) B CD 6 5 3 Check type A Vendor 4 Salary 5 Personal 6 Household 3 4 6 7 5 3 4 5 4 6 a) Find the optimal solution. You need to write down a table for the optimal solution, which includes the number of each type of checks processed at each site, the corresponding unit costs and the minimum total cost. 1.5 pt b) Is there any site which does not run at full capacity? If yes, write down the name of the site(s) and its remaining capacity. 0.5 pt c) Is there any type of checks which cannot be processed at any site? If yes, write down the name of checks. 0.5 pt