An air conditioning manufacturer produces 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 700, and Denver needs 250. Houston has 850 air conditioners available each month, Phoenix has 800, and Memphis has 350. The shipping cost per unit from Houston to Dallas is $8, to Atlanta is $12, and to Denver is $13. The cost per unit from Phoenix to Dallas is $10, to Atlanta is $14, and to Denver is $8. The cost per unit from Memphis to Dallas is $11, to Atlanta is $8, and to Denver is $14. How many units should be shipped from each plant to each regional distribution center? What is the total cost for this?

$16,000

Step-by-step explanation:

For easier understanding and calculation; we created a table for solving this question.

Destination →  Dallas     Atlanta     Denver      Availability

Source

↓                                                                                          

Houston          $ 8         $ 12             $ 13          850          

Phoenix           $ 10       $ 14             $ 8           800            

Memphis         $ 11         $ 8             $ 14          350            

Requirement    800       700            250                            

Minimum Shipping Cost to Dallas is from Houston and they have 850 air conditioners, Dallas need 800, so ship all required 800 air conditioners from Houston itself

Minimum shipping cost of Atlanta is from Memphis and they have 350 air conditioners, but Atlanta need 700, so ship all the 350 air conditioners that Memphis have to Atlanta

Minimum shipping cost to Denver is from Phoenix and they have 800 air conditioners, but Denver need 250, so ship all the required 250 air conditioners to Denver itself.

Destination →  Dallas     Atlanta     Denver      Availability

Source

↓                                                                                          

Houston          $ 8         $ 12             $ 13          850          

                        (800)                                                          

Phoenix           $ 10       $ 14             $ 8           800        

                                                        (250)                            

Memphis         $ 11         $ 8             $ 14          350            

                                      (350)                                                

Requirement    800       700            250                            

Still Atlanta need 350 air conditioners more, the second minimum shopping cost to Atlanta is from Houston and they have 50 air conditioners left .

So, ship all the 50 air conditioners that Houston have to Atlanta

Also, sent the remaining 300 air conditioners that Atlanta need from Phoenix

Destination →  Dallas     Atlanta     Denver      Availability

Source

↓                                                                                          

Houston          $ 8         $ 12             $ 13          850          

                        (800)      (50)                                                

Phoenix           $ 10       $ 14             $ 8           800        

                                     (300)           (250)                            

Memphis         $ 11         $ 8             $ 14          350            

                                      (350)                                                

Requirement    800       700            250                            

The total cost of shipping = ($ 8 × 800) +( ( $ 12 × 50)+($ 14 × 300) +( $ 8 × 350) ) + ( $ 8 × 250)

= ( $ 6, 400) + $ ( 600 + 4, 200 + 2, 800 ) + $ 2, 000

= $ 16,000

Therefore, the total cost = $ 16,000

25

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