You are the Director of Infrastructure Management at the Nash Telecommunications Company. You are tasked with creating their wireless network by building cellphone towers throughout the Greater Toronto Area. Each tower costs $50000 to build. Moreover, maintenance on the first tower costs $500/month, and increases by 25% for each tower that is built. Hence if you build two towers, your total monthly operating costs are $500 1.25 = $625/month. Each tower that you build reaches 500 unique customers, and your company charges $40/month for cellphone services. Determine the number of cellphone towers that you should build in order to maximize your profit in the first year.