• The 1,000 residents of Great Donut Island are all fishermen. Every morning they go to the nearest port to launch their fishing boats and then return in the evening with their catch. The residents are evenly distributed along the 10-kilometer perimeter of the island. Each port has a fixed cost of 1,000/day. If the optimal number of ports is 2, what must be the per kilometre travel cost?
• ANSWER: The population is L = 1,000 and the travel cost is denoted by t. The total travel cost is (L)(t)(10/2N) = 1000t(10/2N) = 5000t/N.
• Total fixed cost is 1000N. Total cost = 5000t/N + 1000N. For the moment, assume that t is known and you are finding the optimal N. So take the first derivative, set it equal to zero,and solve for N. dTC/dN=1000-5000t/N2 =0 so5000t/N2 =1000or t= 1000N2/5000
• Since N = 2, t = 4/5.
• Please explain the theory first step by7 step and then explain the answer in details, thank you!