Over the past decade, the number of uninsured individuals has risen rapidly in the Roanoke region

of Virginia, placing a significant strain on the region$$s only safety net hospital, Roanoke Medical

Center. To help provide primary care services and chronic disease management services to this

population and alleviate some of the strain on the hospital$$s emergency room, the Roanoke Medical

Center is partnering with a national religious health association to establish a free clinic in the

region. Three potential clinic locations are currently under consideration: Cherry Hill Commons,

Eastgate, and Kenwood. On average, clinic patients are expected to contribute $$10$ per visit,

irrespective of location. Annual donations at each location are expected to be $$1$ million, and are

expected to grow $15$ percent annually over the next three years. Although most clinical services are

provided by volunteers, the free clinic will have a salaried executive director, volunteer coordinator,

two full$-$time clinicians, and two part$-$time clinicians, for a total annual cost of $$275,000.$ Fixed

costs, not including salaries, at Cherry Hill are expected to be $$340,000$; fixed costs at Eastgate

are expected to be $$410,000$; and fixed costs for Kenwood are expected to be $$378,000.$ Average

variable costs per visit are expected to be $$20$ at Cherry Hill, $$27$ at Eastgate, and$$24$ at the

Kenwood location. Expected annual patient visits at the Cherry Hill location are $6,180$; expected

annual visits at Eastgate are $5,925$; and expected annual visits at Kenwood are $6,220.$

$($a$)$ Which location should be chosen based on total costs in year $1$ of operations?

$($b$)$ Which location should be chosen based on total profits in year $1$ of operations?

Assume that by year $3$ of operations, health care reform is expected to significantly reduce the

number of uninsured in the Roanoke region. However, an influx of illegal immigrants $-$ who are

not eligible for insurance under health care reform $-$ is also expected to occur, particularly near

$1$

the Cherry Hill location. Accordingly, annual patient visits in year $3$ are expected to be as follows:

$6,745$ at Cherry Hill, $5,750$ at Eastgate, and $5,825$ at Kenwood. To accommodate this increased

patient demand, Cherry Hill will need to bring on additional full$-$time employees $($FTEs$),$ increasing

total fixed costs to $$685,000.$

$($c$)$ Which location should be chosen based on total costs in year $3$ of operations?

$($d$)$ Which location should be chosen based on total profits in year $3$ of operations?

$($e$)$ Determine the sensitivity of the decision in part $($d$)$ to a $\backslash$pm $10$ percent fluctuation in visits.