The first picture is what I need to know for the second picture I posted. The an
ID: 2882520 • Letter: T
Question
The first picture is what I need to know for the second picture I posted.
The annual profit Pin dollars of nursing homes in a region is given by the unction P r, s, t = 0.008253w- 678r1 089s0.877 2.491 where w s the average hourly wage of nurses and aides (in dollars), r is 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 $22 an hour, a reimbursement rate index of 10, an occupancy rate of 85%, and 290,000 ft-of a) Estimate the nursing home's annual profit. The nursing home's annual profit approximately $ 2,241,409 (Do not round until the final answer. Then round to the nearest dollar as needed.) b) Find the four partial derivatives of P OP ow (Simplify your answer. Use integers or decimals for any numbers in the expression. Round to six decimal places as needed.) 0.005596w-1.878 r1.089 s0.377t2.491 T= 0.008822w-0.878 .089 s0.877t2.491 Simplify your answer. Use integers or decimals for any numbers in the expression. Round to six decimal places as needed.) aP = 0.007238w-0.678 r 1.089s-o. 123t2.491 ds (Simplify your answer. Use integers or decimals for any numbers in the expression. Round to six decimal places as needed.) OP = 0.020558w-0.878 r1.089s0.377 t1.491 ot Simplify your answer. Use integers or decimals for any numbers in the expression. Round to six decimal places as needed.)Explanation / Answer
w = 20
r = 60
s = 310000
t = 10
a)
Profit = 0.007302 w^-0.658 *r^1.041*s^0.826 * t^2.467
= 0.007302 (20)^-0.658 *(60)^1.041*(310000)^0.826 * (10)^2.467
= $ 726581
b)
dp/dw = 0.007302*(-0.658 )w^-0.342 *r^1.041*s^0.826 * t^2.467
= -0.004805 w^-1.658 *r^1.041*s^0.826 * t^2.467
dp/dr = 0.007302*1.041*w^-0.658 *r^0.041*s^0.826 * t^2.467
=0.0076014*w^-0.658 *r^0.041*s^0.826 * t^2.467
dp/ds = 0.007302*0.826*w^-0.658 *r^1.041*s^-0.174 * t^2.467
= 0.006031*w^-0.658 *r^1.041*s^-0.174 * t^2.467
dp/dt = 0.007302*2.467 w^-0.658 *r^1.041*s^0.826 * t^1.467
= 0.01801 w^-0.658 *r^1.041*s^0.826 * t^1.467
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