Math, microeconomics

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 740 homeless patients and no more than 800 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 $9,600 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $7,600 per month. How many of each type of patient should it house in order to maximize profit? (If an answer does not exist, enter DNE.)

high-income patients ......

homeless patients ........

profit $......

Answer 1

x>/= 740

y</= 800

x+y= 1800

x</=2y

x=1200

y=600

9600(1200)+7600(600)

= ,11,520,000+4,560,000

= $16,080,000

1200 homeless, 600 high income

9600(1000)+7600(800)

=9600000+6080000

=$15,680,000