A group of traders are leaving Switzerland, and need to convert their Francs into various international currencies. There are n traders t1; t2; :::; tn and m currencies c1; c2; :::; cm. Trader tk has Fk Francs to convert. For each currency cj , the bank can convert at most Bj Franks to cj . Trader tk is willing to trade as much as Skj of his Francs for currency cj.(For example, a trader with 1000 Francs might be willing to convert up to 200 of his Francs for USD, up to 500 of his Francs for Japanese's Yen, and up to 200 of his Francs for Euros). Assuming that all traders give their requests to the bank at the same time, design an algorithm that the bank can use to satisfy the requests (if it is possible). 1. Describe how to construct a flow network.
2. Make a claim. Something like "this problem has a feasible solution if and only if the max flow is ..."
3. Prove the above claim in both directions.

Anew author is in the process of negotiating a contract for a new romance novel. the publisher is offering three options. in the first option, the author is paid $5,000 upon delivery of the final manuscript and $20,000 when the novel is published. in the second option, the author is paid 12.5% of the net price of the novel for each copy of the novel sold. in the third option, the author is paid 10% of the net price for the first 4,000 copies sold, and 14% of the net price for the copies sold over 4,000. the author has some idea about the number of copies that will be sold and would like to have an estimate of the royal- ties generated under each option. write a program that prompts the author to enter the net price of each copy of the novel and the estimated number of copies that will be sold. the program then outputs he royalties under each option and the best option the author could choose. (use appropriate named constants to store the special values such as royalty rates and fixed royalties.