An air conditioning manufacturer produces room air conditionersat plants in Houston, Phoenix, and Memphis. These are sent toregional distributors in Dallas, Atlanta, and Denver. The shippingcosts vary, and the company would like to find the least-cost wayto meet the demands at each of the distribution centers. Dallasneeds to receive 800 air conditioners per month, Atlanta needs 600,and Denver needs 200. Houston has 850 air conditioners availableeach month, Phoenix has 650, and Memphis has 300. The shipping costper unit from Houston to Dallas is $8, to Atlanta is $12, and toDenver is $10. The cost per unit from Phoenix to Dallas is $10, toAtlanta is $14, and to Denver is $9. The cost per unit from Memphisto Dallas is $11, to Atlanta is $8, and to Denver is $12. How manyunits should be shipped from each plant to each regionaldistribution center? What is the total cost for this? I need thelinear programming model for this problem and written variables,constraints, and minimize cost.
