The Megabuck Hospital Corp. is to build a state-subsidizednursing home catering to homeless patients as well as high-incomepatients. State regulations require that every subsidized nursinghome must house a minimum of 700 homeless patients and no more than620 high-income patients in order to qualify for state subsidies.The overall capacity of the hospital is to be 1,800 patients. Theboard of directors, under pressure from a neighborhood group,insists that the number of homeless patients should not exceedtwice the number of high-income patients. Due to the state subsidy,the hospital will make an average profit of $13,000 per month forevery homeless patient it houses, whereas the profit perhigh-income patient is estimated at $9,000 per month. How many ofeach type of patient should it house in order to maximizeprofit?
