Assignment:
An air conditioning manufacturer produces room air conditioners at plants in Houston, Phoenix, and Memphis. These are sent to region 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 600, and Denver needs 200. Houston has 850 air conditioners available each month, Phoenix has 650, and Memphis has 300. This shipping cost per unit from Houston to Dallas is $8, to Atlanta is $12, and to Denver is $10. The cost per unit from Phoenix to Dallas is $10, to Atlanta is $14, and to Denver is $9. The cost per unit from Memphis to Dallas is $11, to Atlanta is $8, and to Denver is $12.
a. How many units should be shipped from each plant to each region distribution center?
b. What is the total cost for this?
Provide complete and step by step solution for the question and show calculations and use formulas.