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?
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?
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