Question

An automobile company produces cars in Los Angeles and Detroit and has a warehouse in Atlanta. The company supplies cars to customers in Houston and Tampa. The costs of shipping a car between various points are listed in the file P14_87.xlsx, where a blank means that a shipment is not allowed. Los Angeles can produce up to 1100 cars, and Detroit can produce up to 2900 cars. Houston must receive 2400 cars, and Tampa must receive 1500 cars. a. Determine how to minimize the cost of meeting demands in Houston and Tampa. b. Modify the answer to part a if shipments between Los Angeles and Detroit are not allowed. c. Modify the answer to part a if shipments between Houston and Tampa are allowed at a cost of $5 per car.

Unit shipping costs
		To
		LA	Detroit	Atlanta	Houston	Tampa
From	LA		$140	$100	$90	$225
	Detroit	$145		$111	$110	$119
	Atlanta	$105	$115		$113	$78
	Houston	$89	$109	$121
	Tampa	$210	$117	$82

Answer 1

Here the supply of 4,000 cars and the demand is 3,900. In this case, we add a dummy demand point of 100 cars. For the balanced transportation tableaus and the letter, M represents a large integer that models non-permissible shipments. The given situation is represented below,

Part A

	LA	Detroit	Atlanta	Houston	Tampa	Dummy
LA	0	$140	$100	$90	$225	0	5,100
Detroit	$145	0	$111	$110	$119	0	6,900
Atlanta	$105	$115	0	$113	$78	0	4,000
Houston	$89	$109	$121	0	M	0	4,000
Tampa	$210	$117	$82	M	0	0	4,000
	4,000	4,000	4,000	6,400	5,500	100

Part B

	LA	Detroit	Atlanta	Houston	Tampa	Dummy
LA	0	M	$100	$90	$225	0	5,100
Detroit	M	0	$111	$110	$119	0	6,900
Atlanta	$105	$115	0	$113	$78	0	4,000
Houston	$89	$109	$121	0	M	0	4,000
Tampa	$210	$117	$82	M	0	0	4,000
	4,000	4,000	4,000	6,400	5,500	100

Part C

	LA	Detroit	Atlanta	Houston	Tampa	Dummy
LA	0	$140	$100	$90	$225	0	5,100
Detroit	$145	0	$111	$110	$119	0	6,900
Atlanta	$105	$115	0	$113	$78	0	4,000
Houston	$89	$109	$121	0	$5	0	4,000
Tampa	$210	$117	$82	$5	0	0	4,000
	4,000	4,000	4,000	6,400	5,500	100