There are n cities on a highway with coordinates x1, . . . , xn and we aim to build K < n fire stations to cover these cities. Each fire station has to be built in one of the cities, and we hope to minimize the average distance from each city to the closest fire station. Please give an algorithm to compute the optimal way to place these K fire stations. The algorithm should run in O(Kn^2) time.

In december of 2004, the company you own entered into a 20-year contract with a grain supplier for daily deliveries of grain to its hot dog bun manufacturing facility. the contract called for "10,000 pounds of grain" to be delivered to the facility at the price of $100,000 per day. until february 2017, the supplier provided processed grain which could easily be used in your manufacturing process. however, no longer wanting to absorb the cost of having the grain processed, the supplier began delivering whole grain. the supplier is arguing that the contract does not specify the type of grain that would be supplied and that it has not breached the contract. your company is arguing that the supplier has an onsite processing plant and processed grain was implicit to the terms of the contract. over the remaining term of the contract, reshipping and having the grain processed would cost your company approximately $10,000,000, opposed to a cost of around $1,000,000 to the supplier. after speaking with in-house counsel, it was estimated that litigation would cost the company several million dollars and last for years. weighing the costs of litigation, along with possible ambiguity in the contract, what are three options you could take to resolve the dispute? which would be the best option for your business and why?

Your uncle borrows $53,000 from the bank at 11 percent interest over the nine-year life of the loan. use appendix d for an approximate answer but calculate your final answer using the formula and financial calculator methods. what equal annual payments must be made to discharge the loan, plus pay the bank its required rate of interest

Table 1. shows the expected demand for the dvd at different suggested donation levels, and they can act as a single-price monopolist if they choose to. thereceipts will be used to fund gstcg supplies for their data collection and conservation work. at the end of each sea turtle nesting season, any excess funds are donated by the gstcg to a local non-profit sea turtle research and rehabilitation facility. table 1 suggested anticipated total marginal profit donation per number of dvd revenue revenue dvd request requests $19.00 0 $15.00 2 $9.50 4 $7.75 10 $3.00 15 $0.00 20 a. complete table 1 by computing the total revenue, marginal revenue, and profit columns. b. the president wants the gstcg to provide videos to generate the most possible donations (total revenue). what price, if any, is the president of the gstcg favoring and how many people will receive the dvd if this becomes the price of the suggested donation? explain your answer. c. the education outreach committee wants the gstcg to provide videos to the highest possible number of people. what price, if any, is the educational outreach committee favoring and how many people will receive the dvd if this becomes the price of the suggested donation? explain your answer. d. the treasurer of the gstcg wants the dvd program to be as efficient as possible so that the marginal revenue equals marginal cost. what price, if any, is the treasurer favoring and how many people will receive the dvd if this becomes the price of the suggested donation? explain your answer. e. the fundraising committee wants the dvd program to generate as much profit in donations as possible. what price, if any, is the fundraising committee favoring and how many people will receive the dvd if this becomes the price of the suggested donation? explain your answer.