Assume that a nursing home has two categories of payers

Assume that a nursing home has two categories of payers. Medicaid pays $60 per day, and private-pay patients pay the established per diem. However, approximately 10 percent of private-pay charges are not collected. Variable costs are $45 per day, and fixed costs are expected to be $1 million. Expected volume is 50,000 patient days. If 50 percent of the patients are Medicaid, and 50 percent are private pay, what rate must be set to generate $150,000 in profit?