You work for silver satellite and cable company in research and development department. You have been inquired to come up with the formula to find out cost of running cable from the connection box along the existing highway box to the new house. First example which you are working with involves stevens family, who own rural home with straight driveway 2 miles long extending to house from nearby highway. Nearest existing connection box is along highway 5 miles fromt he driveway. It costs company $1000 per mile to install cable highway and $1400 per mile off highway due to extra permits that county needs. Because stevens house surrounded by farmland which they own, it would be possible to run cable to house directly from connection box or from any point between box to driveway ( along the main highway).
1. Draw the sketch of the problem situation, suppose that highway is the straight road and driveway is straight road perpendicular to highway.
2. Draw the picture for every senario explained below and then find the cost.
a. Consider running cable directly from existing box straight to house.
b. Let running cable 1 mile along highway and then turning off road and going directly to house.
c. Let running cable 2 miles along highway and then turning off road going directly to house.
d. Let running cable along highway all way to driveway, then to house along driveway (off highway).
3. Develop the model: doing part 2 must have helped you see pattern of how to find cost. Now generalize and find cost if wore runs x miles along highway. In other words, make the function to express total cost c(x) ( in dollars) of installation as the function of distance x (length of wire along the highway, in miles).
4. verify the model: use the equation from part 3 to verify values you created in investigation in part 2.
5. Find contextual domain of function you created in part 3 considering application for which it is being utilized?
6. Before proceeding further with installation, you check local regulations and determine that there is pending state legislation which says cable can't turn off highway more than 0.5 mile from stevens driveway. If legislation passes, find ultimate (minimum) cost of installing cable?