It costs $$40$ to buy a telephone from the department store. Assume that I can keep a telephone

for at most five years and that the estimated maintenance cost each year of operation is as

follows: year $1,$ $$20$; year $2,$ $$30$; year $3,$ $$40$; year $4,$ $$60$; year $5,$ $$70.$ I have just purchased a

new telephone. Assuming that a telephone has no salvage value, determine how to minimize the

total cost of purchasing and operating a telephone for the next six years. Consider the problem

as finding a shortest path and apply Dijkstra's Algorithm to find the optimal solution.