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Price to be charged

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Here is the question:
The Sans Roentgen Outpatient MRI Center has asked you to detemine the price to be charged for each MRI scan for the first year of operations. Below is the relevant budget data:
DESCRIPTION BUDGET
Cost-------------------------------------------------------$2,100,000
Volume-----------------------------------------------------3,650
Medicare Mix-----------------------------------------------60%
Private Insurance Mix--------------------------------------40%
Medicare Payment Per Procedure-----------------------------$650
Private Insurance Pays-------------------------------------85% of charges
Desired Profit---------------------------------------------$500,000
In 700-1000 words please help me explain what price the MRI Center must charge in order to meet its desired profit of $500,000. Be sure to include all calculations and rationales behind your answer. I need help with this, I am not sure where to even start. Any help you could give me would be greatly appreciated.

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The solution explains how to determine the price to be charged given the costs and desired profit.

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The price to be charged should be such that it meets all the costs and also results in a profit of $500,000. The cost for the year is $2,100,000. The total income from the charge should be

2,100,000+500,000=2,600,000.

We are also given that the total number of procedures to be done are 3,650. We can straight away get the cost per procedure to be

2,600,000/3,650=$712.32.

This would not be correct, since there are two distinct groups which pay at different rates. The Medicare will pay a flat rate of $650 and the private insurance will pay 85% of the charge. The income is ...

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