A healthcare provider offers a single service to its patients, and the patients are covered by only two different third parties. Payer 1, Medicare, represents 50% of the patients and pays a fixed fee of $60 per patient. Payer 2, a Commercial Insurer, represents 40% of the patients and pays 80% of the provider's gross charge. The remaining patients are Charity Care patients who do not pay for their services. The provider treats 8,000 patients per month. The fixed costs of the provider each month is $166,000, and their variable cost per patient is $40. The provider desires to set its gross charge per patient to achieve a profit, or net income, of $10,000 for the month.
a. Set up an Algebraic expression, with "p" being the gross charge (price) of the service to each patient being seen in the month, to solve this problem.
b. Solve the problem finding the Gross Price to be charged. (Show your work as partial credit will be given.)
c. How many charity patients does the organization treat per month?
What is the grand total of payments that the Commercial Insurer pays for all of its patients in a month? (Note, this is not the total for one patient, but instead it is the total for all of their patients in the month).