Question

The annual profit P (in dollars) of nursing homes in a region is given by the function P[w.r. 8. t) = 0.007453w - 0,646,1.026 0.844,2.489 where w is the average hourly wage of nurses and aides (in dollars), ris the occupancy rate (as a percentage), s is the total square footage of the facility, and t is a number between 1 and 11 that measures the reimbursement rate in the region. A certain nursing home has nurses and aides with an average hourly wage of $20 an hour, a reimbursement rate index of 10, an occupancy rate of 60%, and 360,000 ft of space. a) Estimate the nursing home's annual profit. The nursing home's annual profit approximately $ (Do not round until the final answer. Then round to the nearest dollar as needed.)

Answer 1

The annual profit P, in dollars, of nursing homes in a region is given by the function

$\small P(w,r,s,t)=0.007453w^{-0.646}r^{1.026}s^{0.844}t^{2.489}$

where w is the average hourly wage of nurses and aides, which in our case, is given to be $20

r is the occupancy rate, which is given as 60%

s is the total square footage of the facility, which is given as 360,000 square feet

and, t is the reimbursement rate in the region, which is given as 10.

Hence, the profit P using these values of w,r,s and t, is

$\small P(20,60,360000,10)=0.007453\left(20\right)^{-0.646}\left(60\right)^{1.026}\left(360000\right)^{0.844}\left(10\right)^{2.489}$

$\small =0.007453\cdot \:145357390.01759$

$\small =1083348.62780$

Thus, the nursing homes annual profit is approximately $1083349