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 730 homeless patients and no more than 1,100 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 2,400 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 $9,900 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $7,900 per month How many of each type of patient should it house in order to maximize profit? HINT [See Example 3.] (If an answer does not exist, enter DNE.) high-income patients homeless patients profit $

As maximum profit per patient is on homeless patient, and homeless patient cannot be more than 1,600 as because of the management decided ratio of high income patient and homeless patient.

Profit in this case,

Homeless patient = [tex]1,600 \times 9,900 = 15,840,000[/tex]

High income patient = [tex]800 \times 7,900 = 6,320,000[/tex]

Total profit = $22,160,000

andromache andromache · Answer 2 · 2022-01-21T14:24:41+01:00

High income patient = 800

Homeless patient = 1,600

The calculation is as follows:

Here we assume high income patients be

So, homeless patients be 2x

And, Total patients = 2,400

Now,

x + 2x = 2,.400

3x = 2,400

x= 800

so, the homeless patient should be 2(800) = 1,600

Now

Profit in this case,

Homeless patient = 1,600 (9900) = 15,840,000

High income patient = 800 (7,900) = 6,320,000

Total profit = $22,160,000

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