HSA, a local hospital system has set up a new vaccination facility for a virus that is causing serious illness in the region.

The total cost for the set up is $300,000. The hospital system services patients with all types of insurance. They would like to make $10,000 extra income at the end of the year. In terms of the number of patients, they have Medicare (30%), and Medicaid (25%), Managed Care Type I (5%), Managed Care type II (35%), and Uninsured (5%).

The first three categories have fixed payment rates, for Medicare $180, Medicaid $170, and Managed care Type I $225. The other two pay based on the hospital charges (or prices). Managed Care Type 2 pays 80% of the charges and the Uninsured pay on an average 10% of the charges.

The expected annual volume is 2000.

1. Determine the price (charges) the hospital system can charge for the vaccination to obtain the desired extra income.
2. Using the price obtained in part (a) compute the total income the hospital can get, and show that with the targeted price, it can get the $10,000 extra income.