Personal Computer Inc., produces up to 5000 computers in Boston and up to 3500 computers in Raleigh each year. Los Angeles customers must receive 2300 computers, 3700 computers must be supplied to New York customers, and Seattle customers must be supplied 1300 computers. Producing a computer costs $250 in Boston and $275 in Raleigh. Computers are transported by plane and can be sent through Chicago. The costs of sending a computer between pairs of cities are given below: ---------------------------------------------------------To -------------------------Chicago----Los Angeles----New York----Seattle ------------Boston-------$40----------$80--------------$30-------------$75 From----Raleigh -----$45----------$75--------------$55-------------$85 ------------Chicago-------$0-----------$65--------------$45-------------$60 a. Determine how to minimize the total (production plus distribution) cost of meeting Personal Computer Inc.s annual demand. Why doesn't it make any sense to ship any computers through Chicago?

b. How would you modify the model in part a if no more than 1250 computers could be shipped between any two cities, and what would be the optimal solution to the modified model? Why are computers now shipped through Chicago?

A1 X for Computer production and shipping D E F G H J K A B 1 Computer production and shipping 2 3 Unit shipping costs 4 5 Chicago 6 From Boston 7 Raleigh 8 Chicago Los Angeles New York Seattle City indexes Boston Raleigh Chicago Los Angeles New York Seattle 9 Total cost Flow Capacity Required 10 Unit production costs 11 Boston 12 Raleigh 13 14 Flows 15 Origin Destination Production cost Shipping cost 16 Boston Chicago 17 Boston Los Angeles 18 Boston New York 19 Boston Seattle 20 Raleigh Chicago 21 Raleigh Los Angeles 22 Raleigh New York 23 Raleigh Seattle 24 Chicago Los Angeles 25 Chicago New York 26 Chicago Seattle 27 28 Total cost Flow balance constraints City Outflow Boston Raleigh Net outflow Chicago Inflow Los Angeles New York Seattle Demand 29 30 31 32 33 34 35 36 37 A1 X for Computer production and shipping D E F G H J K A B 1 Computer production and shipping 2 3 Unit shipping costs 4 5 Chicago 6 From Boston 7 Raleigh 8 Chicago Los Angeles New York Seattle City indexes Boston Raleigh Chicago Los Angeles New York Seattle 9 Total cost Flow Capacity Required 10 Unit production costs 11 Boston 12 Raleigh 13 14 Flows 15 Origin Destination Production cost Shipping cost 16 Boston Chicago 17 Boston Los Angeles 18 Boston New York 19 Boston Seattle 20 Raleigh Chicago 21 Raleigh Los Angeles 22 Raleigh New York 23 Raleigh Seattle 24 Chicago Los Angeles 25 Chicago New York 26 Chicago Seattle 27 28 Total cost Flow balance constraints City Outflow Boston Raleigh Net outflow Chicago Inflow Los Angeles New York Seattle Demand 29 30 31 32 33 34 35 36 37