Question

Allen Air Conditioning manufactures room air conditioners at plants in Houston?, Phoenix?, and Memphis. These are sent to regional distributors in Dallas?, Atlanta?, and Denver. The shipping costs? vary, and the company would like to find the least cost way to meet the demands at each of the distribution centers.??Dallas needs to receive 800 air conditioners per? month, Atlanta needs 500?, and Denver needs 350. Houston has 850 air conditioners available each? month, Phoenix has 650?, and Memphis has 300. The shipping cost per unit from Houston to Dallas is ?$8?, to Atlanta ?$12?, and to Denver ?$10. The cost per unit from Phoenix to Dallas is ?$10?, to Atlanta ?$14?, and to Denver ?$9. The cost per unit from Memphis to Dallas is ?$11?, to Atlanta ?$8?, and to Denver ?$12.

1) Based on the given demand and? supply, the given transportation problem is ......................  Balanced or Unbalance??

2) How many units should be shipped from each plant to each regional distribution center?

3) What is the total cost for this?

Answer 1

1) As the Demand of Air condition < Supply of Air conditioner, the Transportation Problem is Unbalance.

2)

The Initial Table can be drawn as follows-

The Lowest cost in the cost section corresponds to 1x1. Assigning supply responsibility based on Supply & Demand Constraint ( such that supply is less than or equal to Max Supply or Max Demand), we get-

The Lowest cost in the cost section corresponds to 3x2. Assigning supply responsibility based on Supply & Demand Constraint ( such that supply is less than or equal to Max Supply or Max Demand), we get-

The Lowest cost in the cost section corresponds to 2x3. Assigning supply responsibility based on Supply & Demand Constraint ( such that supply is less than or equal to Max Supply or Max Demand), we get-

The Lowest cost in the cost section corresponds to 1x2 but we only have a supply of 50 available. Thus for the impending 150 demand, we will assign this responsibility to 2x2. Thus, we will get-

Therefore the assignment is-

800 units from Houston to Dallas, 50 units from Houston to Atlanta, 150 units from Pheonix to Atlanta, 350 units from Pheonix to Denver and 300 units from Memphis to Atlanta.

The Total Cost will be - 800*8+50*12+14*150+300*8+350*9 = 14650

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