Dr$.$ Na Gu plans to open a radiology office that provides CAT scans. She can lease the CAT scanner for $$1,200$ per month plus $$45$ for each imaging session. In addition to the $$45$ lease cost per imaging session, Dr$.$ Gu must purchase film for each session at a cost of $$55.$ She plans to charge $$250$ for each session. Dr$.$ Gu has identified a suitable office that she can rent for $$1,400$ per month. The monthly cost of a receptionist is $$2,400$ and two radiology technicians are $$3,200$ each per month.

Office furnishings, phones, and office equipment cost $$600$ per month. She expects that her salary will be $$15,000$ per month.

Required:

How many imaging sessions per month must Littleton Imaging conduct in order for the office to break even?

How many imaging sessions per month must Littleton Imaging conduct in order for the office to yield an after$-$tax profit of $$5,000$ if the tax rate is $25$ percent?

Dr$.$ Gu expects that the office will perform $200$ imaging sessions per month. How much must she charge per session to break even?