Question

Part 4.     Bank Assignments. A bank distributes checks to different sites to be processed within a large metro area. Each site has the capacity to process different amounts of checks per day. The checks that need to be processed each day are personal, payroll, draft, and government. The total demand is different for each type of check. The cost to process each type of check varies with the site. These values are summarized in the table.

Cost per check	Site1	Site2	Site3	Site4	Site5	Total Demand Checks/day
Personal	2.55	2.35	3.22	2.85	2.25	700
Payroll	1.45	1.35	2.1	1.95	1.84	400
Draft	1.67	1.51	1.89	1.86	1.78	200
Government	1.34	1.35	1.41	1.3	1.33	100
Total Capacity Checks/day	500	300	300	200	200

Question 1a. What is the minimum cost that can be achieved and meet requirements?

A. $2680    B. $2798    C. $2579    D. $2783    E. None of the above

Question 1b. From concern about a site processing a large number of one type of check, a limit of 250 transactions per type of check for each site is being considered. What is the minimum increase in cost due to this added constraint?   A. $20    B. $15    C. $10    D. $5    E. None of the above

Answer 1

Formulation in Excel:

Solver inputs:

Solution:

	Site1	Site2	Site3	Site4	Site5	Total	Demand
Personal	100	300	0	100	200	700	700
Payroll	400	0	0	0	0	400	400
Draft	0	0	200	0	0	200	200
Government	0	0	0	100	0	100	100
Total	500	300	200	200	200
Total Capacity	500	300	300	200	200
COSTS	Site1	Site2	Site3	Site4	Site5
Personal	2.55	2.35	3.22	2.85	2.25
Payroll	1.45	1.35	2.1	1.95	1.84
Draft	1.67	1.51	1.89	1.86	1.78
Government	1.34	1.35	1.41	1.3	1.33
Total cost	2783

So, answer to 1A is 2783

-----------------------

1B

Add the following constraint to solver:

Solution:

	Site1	Site2	Site3	Site4	Site5	Total	Demand
Personal	250	150	0	100	200	700	700
Payroll	250	150	0	0	0	400	400
Draft	0	0	200	0	0	200	200
Government	0	0	0	100	0	100	100
Total	500	300	200	200	200
Total Capacity	500	300	300	200	200
COSTS	Site1	Site2	Site3	Site4	Site5
Personal	2.55	2.35	3.22	2.85	2.25
Payroll	1.45	1.35	2.1	1.95	1.84
Draft	1.67	1.51	1.89	1.86	1.78
Government	1.34	1.35	1.41	1.3	1.33
Total cost	2798

So,

The cost increases by 2798 - 2783 = 15