The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 700 homeless patients and no more than 620 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 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. Due to the state subsidy, the hospital will make an average profit of $13,000 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $9,000 per month. How many of each type of patient should it house in order to maximize profit ?
A)1,200 homeless patients and 600 high-income patients
B) 700 homeless patients and 350 high-income patients
C) 700 homeless patients and 1,100 high-income patients
D) 1,180 homeless patients and 620 high-income patients
E) no solution

Question

The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 700 homeless patients and no more than 620 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 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. Due to the state subsidy, the hospital will make an average profit of $13,000 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $9,000 per month. How many of each type of patient should it house in order to maximize profit  ?
A)1,200 homeless patients and 600 high-income patients
B) 700 homeless patients and 350 high-income patients
C) 700 homeless patients and 1,100 high-income patients
D) 1,180 homeless patients and 620 high-income patients
E) no solution

Quizplus · Accepted Answer

To maximize profit while adhering to the constraints, the hospital should house 1,200 homeless patients and 600 high-income patients. This configuration respects the state's regulations, the hospital's capacity, and the board's requirement that the number of homeless patients not exceed twice the number of high-income patients, while also maximizing profit based on the profit margins provided for each patient type.