Question

The Megabuck Hospital Corp. is to build a state-subsidized mursing home catering to homeless patients as weil as lighemincome patieni. capacity of the hospital is to be 2,400 patients. The board of directors, under pressure frem a neighborhood group, insists that the number of homeless patients should not. exiceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of s9,600 per month for every homeless patient it houses, whereas the profit pec 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?

Answer 1

Megabuck Hospital Corp should optimize the number of homeless and high-income patients to house within their capacity of 2,400, considering their profit margins (homeless: $9,600/month, high-income: $7,800/month) and the restriction that homeless patients cannot exceed twice the number of high-income patients.

The task is to determine the number of homeless and high-income patients the Megabuck Hospital Corp should house to maximize profit, while adhering to the constraint that the number of homeless patients should not exceed twice the number of high-income patients. The capacity of the hospital is 2,400 patients. Let H represent the number of homeless patients and I represent the number of high-income patients. The following constraints arise:

• H + I ≤ 2,400 (capacity constraint)
• H ≤ 2I (board restriction)

The profit function to maximize is P = 9,600H + 7,800I. To solve this, we apply linear programming techniques, which may include graphical methods or optimization software. Once solved, we can state the optimal number of each patient type required to achieve maximum profit.

The answer will be expressed as the number of homeless patients and the number of high-income patients that should be housed.