Answered: The Megabuck Hospital Corp. is to build…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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 760 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 2,100 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 $9,800 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $7,800 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

Expert Solution

Step 1: Introduction of the given problem

Nursing home must house a minimum of $760$ homeless patients and no more than $800$ high-income patients

The overall capacity of the hospital is to be $space 2 comma 100 space$ patients.

The number of homeless patients should not exceed twice the number of high-income patients.

The hospital will make an average profit of $$ 9 comma 800$ per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $$ 7 comma 800$ per month