# calculus

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You work for the silver there is a home with a driveway 2 miles long extending to the house from a nearby highway. the nearest connection box is along the highway but 5 miles from the driveway. it costs the company \$100 per mile to install cable along the highway and \$140 per mile to install cable off the highway.

a) make a table of the possible integral values of x and the corresponding cost in each instance. does one choice appear to cost the least?

b) if you charge the owners of the house \$800 for installation, would you be willing to let them choose which way the cable would go? explain

c) using a graphing calculator, graph the function and determine the value of X that would make the installation cost minimum?

d) check the local regulations for cable companies and find that there is pending state legislation that says that the cable that the cable cannot turn off the highway more than 0.5 mile from the house's driveway. if this legislation passes, what will be the ultimate cost of installing the house's cable?

e) if the cable companhy wishes to install cable in 5000 homes in this area, and assuming that the figures for the original house's installation are typical, how much will the new legislation cost the company overall if they cannot use the cheapest installation cost, but instead have to follow the new state regulation?