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 600, and Denver needs 200. Houston has 750 air-conditioners available each month, Phoenix has 550, and Memphis has 300. The shipping cost per unit from Houston to Dallas is $8, to Atlanta is $12, and to Denver is $10. Due to truck capacity limits, no more than 50 air-conditioners can be shipped between Houston and Denver each month. The cost per unit from Phoenix to Dallas is $10, and to Denver is $9. Air conditioners from Phoenix are never shipped to Atlanta. The cost per unit from Memphis to Dallas is $11, to Atlanta is $8, and to Denver is $12. problem:Formulate a linear optimization model to determine how many units should be shipped from each plant to each regional distribution center. You do not need to solve the problem.