Exercises due Oct 1 The classic transportation problem. You as an employee of the Department of Homeland Security (DHS) are in charge of maintaining the readiness of emergency supplies at various distribution sites within a region that may be subjected to natural or human caused disasters. These supplies come from manufacturers located at other sites within a larger region. These supplies need replacing periodically, whether used or not. The problem you face each month is to determine how much of each kind of item needs to be shipped from each ‘supply or warehouse’ site to each distribution site given a varying demand depending on use and obsolescence. At the end of each month the shortage of each type of item at each customer site is sent to you. You also know the total amount of each type of item available at the supply or warehouse sites. Your job is to fill the demand (remove the shortage) at each distribution site at a minimum cost. a) This is what you know at the end of each month: The cost of shipping an amount of item type i (i = A, B) from a supply or warehouse site j to a distribution site k is C(i,j,k). The total amount of item type i at supply site j is S(i,j). The demand for an amount of item type i at distribution site k is D(i,k). Define a model that when solved will give you the least cost way of meeting the demands of all items at all distribution sites for any particular month, assuming the total supply available at all supply sites equals or exceeds the total sum of all demands at all distribution sites k for each item i. Obviously the answer will change in each month as the data about costs, supplies and demands change. But while the data may differ, the model should be the same. Using your model, find the minimum total cost for the following example: 3 warehouse supply sites, 4 demand distribution sites, 2 items (A and B). Try solving it without