The annual profit P (in dollars) of nursing homes in a region is given by the function P(w, r, s, t) = 0.007749w / 2 50 40 where w is the average hourly wage of nurses and aides (ir 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 and aides with an average hourly wage of $17 an hour, a reimbursement rate index of 10, an occupancy rate of 65%, and 450,000 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.) b) Find the four partial derivatives of P. OP aw (Simplify your answer. Use integers or decimals for any numbers in the expression. Round to six decimal places as needed.) OP ar (Simplify your answer. Use integers or decimals for any numbers in the expression. Round to six decimal places as needed.) OP ds (Simplify your answer. Use integers or decimals for any numbers in the expression. Round to six decimal places as needed.) OP at (Simplify your answer. Use integers or decimals for any numbers in the expression. Round to six decimal places as needed.)