Chapter 6.2, Problem 38E

Project Design The Megabuck Hospital Corporation is to build a state-subsidized nursing home serving homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 1,000 homeless patients and no more than 750 high-income patients in order to qualify for state subsidies. The overall capacity of the nursing home is to be 2,1 00 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high income patients. Because of the state subsidy, the nursing home will make an average profit of $10,000 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $8,000 per month. How many of each type of patient should the nursing home house to maximize profit? [HINT: See Example 3.]