You are charged with locating an express mail drop box somewhere on the network shown in Figure XXXXXXXXXXThis is like a mailbox except that only packages that are going out by express mail may be...

You are charged with locating an express mail drop box somewhere on the network shown in Figure 6.35. (This is like a mailbox except that only packages that are going out by express mail may be placed in the box.) You have identified the locations of the largest firms in the area (all law firms). These firms are identified by circled numbers on the following map (e.g., s for the firm of Tort and Retort). Each firm is located at the intersection of two streets as indicated in the following table. The number of packages per day is also given in the following table.

(a) Assuming you can only walk along north–south avenues and east– west streets, find the location of the drop box that minimizes the demand-weighted distance that people must walk from the office to the drop box. Demand is weighted by the number of packages per day. Give the intersection at which the drop box should be located. What is the value of the objective function at this point (assuming that the law firms are at the intersections)?

(b) The demands listed above are the current demands. However, the criminal law firm of Jail Em Fast Ltd. is growing very rapidly. (Note that a recent study showed that the United States has the largest number of imprisoned people per 100,000 in the population of the countries in the study, ahead of Russia by 40%, 2.4 times Iran, and over 6 times Canada, France, Italy, the United Kingdom, and Germany). 1 How large must the number of packages per day delivered from this firm become for it to be optimal to change the location of the drop box? Where would the new drop box be located?