Laying phone cable, continued: This is a continuation . Suppose it costs $300 per mile to run cable on land but $500 per mile to lay it under water.
a. Let C be the total cost of the project, in dollars. Explain why C = 300L + 500W.
b. Write a formula for C as a function of L.
c. Find the amount of cable that runs under water and the total cost of the project if you choose L to be 1 mile long. Draw and properly label a picture that shows this cable plan.
d. Find the amount of cable that runs under water and the total cost of the project if you choose L to be 3 miles long. Draw and properly label a picture that shows this cable plan.
e. Make a graph of the cost C as a function of L, and explain what the graph is showing.
f. What value of L gives the least cost for the project?
g. Find the value of W that corresponds to your answer in part f, and draw a picture showing the least-cost project. h. Potential legal disputes about easements have caused the cost of laying cable on land to increase to $700 per mile. With this change, find a new formula for the cost C. How does this affect your plans for the least-cost project?