In the summer of 1999, construction will begin on a 3000 ft. tunnel that will pass under the Mississippi River, connecting the cities of East St. Louis, Illinois and St. Louis, Missouri. A Missouri-based company has been contracted to begin excavating the tunnel from the Missouri side, while an Illinois-based company will begin from the Illinois side.

The cost of digging the tunnel depends on many factors, including the overall length of the tunnel. However, the cost per unit length is not constant: as the tunnel gets longer, the cost per unit length increases because of the increasing expense of carrying tools and workers in and hauling dirt and rock out. In their initial bids, both companies have suggested that their rates per foot vary linearly with distance. Their rates are summarized in the following table:

The state governments would like to have this project completed in the most cost effective way. That's where we come into the picture.

1. For each company, determine the linear function that gives the cost per foot as a function of distance dug.
2. For each company, determine a function that gives that cost of digging x feet of tunnel. Sketch a graph of each function.
3. For each company, determine the total cost of digging the tunnel if the company works alone.
4. Find the total cost of digging the tunnel if each company digs one-half of the tunnel.
5. Find the point at which the two companies should meet if the overall cost is to be minimized. What is the overall cost in this case?