Total volume

$1,000$

Average cost

$$100$

Payer volumes

Medicare $($payment rate $=$$$95)$

$400$

Medicaid $($payment rate $=$$$75)$

$100$

Managed Care # $1$

$($payment rate $=$$$110$

$300$

Managed Care # $2$

$($pay $80\%$ of charges$)$

$100$

Uninsured $($pay $10\%$ of charges$)$

$100$

Total all payers

$1,000$

Desired net income

$$5,000$

Medicare and Medicaid presently account for $50\%$ of the volume. The hospital wishes to reduce its dependence on government payers. Assume that Medicare volume is reduced to $380$ patients and Medicaid volume is reduced to $90$ patients. The volume from managed$-$care plan #$1$ rises to $320$ patients from $300.$ The volume from managed$-$care plan #$2$ increases to $110$ patients. Thus, total volume is unchanged at $1,000$ visits. What is the new price necessary assuming all other factors are unchanged?