Based on the information given the county's annual profit if they were to process 4,000 prisoners per year at this new location is $50,000.
Annual profit=Total revenue-Total cost
Where:
Total revenue=(4,000×$75)=$300,000
Total cost=[(4,000×$50)+$50,000]=$250,000
Let plug in the formula
Annual profit=(4,000×$75)-[(4,000×$50)+$50,000]
Annual profit=$300,000-($200,000+$50,000)
Annual profit=$300,000-$250,000
Annual profit=$50,000
Inconclusion the county's annual profit if they were to process 4,000 prisoners per year at this new location is $50,000.
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