Ben is planning an event, so he decides to investigate potential catering companies. Company A quotes a price of $1900 and says they will provide staff for food and drink service at an extra cost of $200 per hour, for a minimum of two hours. Company B quotes a price of $2100 and says they will provide staff for food and drink service for $160 per hour for a minimum of one hour and a maximum of six hours.
Write down two functions, including their domains, for the total revenue generated by company A and company B from catering the event.
Ben has already calculated other costs involving in running the event and has concluded that the event needs to be at least three hours long in order to make a profit.
On the same diagram, sketch the graphs of both of the functions found in part (a).
Determine which catering company Ben should use to minimise the cost based on the duration of the event.
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