1. Suppose that a long-term-care facility (LTC) has private demand for beds equal to 100-5p+3q, where p is the private price (in thousands of dollars per year) and q is the quality level at the LTC. There are a total of 100 beds at the LTC, and the facility will admit Medicaid patients to fill all beds not taken by private (non- Medicaid) patients. So the number of Medicaid patients admitted equals 100 - (100-5p+39). The LTC facility has total cost equal to q2. The Medicaid reimbursement rate (i.e. the Medicaid price) is fixed at r (thousand dollars per year). a) Write an expression for the total revenue for the LTC facility. b) Suppose that requals 10. Write an expression for the LTC facility's profit. c) Use calculus to find the first order condition with respect to p. 1. Suppose that a long-term-care facility (LTC) has private demand for beds equal to 100-5p+3q, where p is the private price (in thousands of dollars per year) and q is the quality level at the LTC. There are a total of 100 beds at the LTC, and the facility will admit Medicaid patients to fill all beds not taken by private (non- Medicaid) patients. So the number of Medicaid patients admitted equals 100 - (100-5p+39). The LTC facility has total cost equal to q2. The Medicaid reimbursement rate (i.e. the Medicaid price) is fixed at r (thousand dollars per year). a) Write an expression for the total revenue for the LTC facility. b) Suppose that requals 10. Write an expression for the LTC facility's profit. c) Use calculus to find the first order condition with respect to p