You have been hired as the new CFO at CFO at the East Bay Rehabilitation, a small nursing home. In your new role you have been asked to help set rates to assure the nursing home makes a minimum profit of $$250,000$ per year. East Bay has two categories of payers, Medicaid and private$-$pay patients. Medicaid currently pays $$75\mathrm{.}00$ per day and private pay patients pay the established per diem, but approximately $10\%$ of private$-$pay charges are not collected. If $50\%$ of the patients are Medicaid and $50\%$ are private pay, what rate must be set to generate $$250,000$ in profit? Variable costs are $$55\mathrm{.}00$ per day and fixed costs are expected to be $$1,200,000.$ Expected volume is $60,000$ patient days. Steps are required.