PROBLEM 1
CitiSavings Bill-processing Operations
CitiSavings operates three bill-processing centers as a part of its credit card business. These centers are located in the Los Angeles, Chicago, and New York areas, and they can process the following numbers of bills each day:
Los Angeles
Chicago
New York
Daily bill-processing capacity
60,000
105,000
100,000
Customers from around the country mail payments on their credit card bills to the three centers for processing. The numbers of bills to be processed daily from each region are as follows:

Number to be Processed
West
70,000
Midwest
50,000
East
80,000
South
40,000

When a bill is mailed from a region to a processing center, it spends time in the U.S. Postal Service (USPS) delivery system. The table below shows the average number of days a bill spends in transit between each region and processing center:
Los Angeles
Chicago
New York
West
2
6
8
Midwest
6
2
5
East
8
5
2
South
8
5
5
Each day that a bill spends in transit is a day’s worth of interest CitiSavings has lost on the payment received. At a 5% annual rate, the interest lost on an average payment is approximately 10 cents per day.
CitiSavings has formulated a linear program (LP) to help it determine to which processing center customers from the various regions should mail their payments. CitiSavings would like to minimize the interest income lost due to transit times of the payments. The model they have formulated is as follows:
Xij = number of bills to be mailed from region i to processing center j each day
Min 2 XWL + 6 Xwc + 8 XWN + 6 XML + 2 XMC + 5 XMN +
8 XEL + 5 XEC + 2 XEN + 8 XSL + 5 Xsc + 5 XSN
s.t.

XWL + XML + XEL + XSL = 60,000 (Los Angeles capacity)
Xwc + XMC + XEC + Xsc = 105,000 (Chicago capacity)
XWN + XMN + XEN + XSN = 100,000 (New York capacity)
XWL + Xwc + XWN = 70,000 (West requirements)
XML + XMC + XMN = 50,000 (Midwest requirements)
XEL +…