Metro Media Cable is asked to provide service to a customer

Metro Media Cable is asked to provide service to a customer whose house is located 2 miles from the road along which the cable is buried. The nearest connection box for the cable is located 5 miles down the road (see the figure). If the installation cost is $100 per mile along the road and $140 per mile off the road, express the total cost C of installation as a function of the distance x (in miles) from the connection box to the point where the cable installation turns off the road. C(x) = Compute the cost if x = 1 mile(s). Compute the cost if x = 4 miles.

Solution

Distance between point where cable turns off and house is 2 + (5-x)

Cost for laying along road = $ 100( 5-x)

Cost for laying off the road = $2*140

a) Total cable laying cost = 100(5-x) + 280 = 780 -100x

b) If x=1 mile; Total cost = 780 -100 =$ 680

c) If x= 4 miles ; Total cost = 780 - 100*4 = $ 380