A company handling small tunnel-digging job in the Guadalupe Mountains in West Texas is in need of assistance in as much as their only staff mathematician, Mr. Mole, was murdered while putting the finishing touches on the job. He left only a page of sketchy notes concerning an important upcoming project. The company is requesting your help to finish where Mr. Mole had left off.
The cost of digging a tunnel depends on several factors, including length and diameter of the tunnel and then number of starting points for the tunnel. When one considers just the length when digging a tunnel, the cost per unit length is not constant: as the tunnel gets longer, the cost per unit length increases. This is due to the increasing expense of carrying tools and workers in, laying track and hauling dirt and rock out. This effect is summarized in the chart below which gives cost per foot estimates for digging a 50 foot diameter tunnel.
|Cost per foot ($/ft.)||$500||$820||$1,180||$1,580||$2,020||$2,500||$3,020||$3,580||$4,180||$4,820|
Your job is to answer the following questions concerning the assignment.