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4. (20 marks) After years and years of cuts to its budget, a university library has re- ceived an endowment which generates an annual income of $10,000. The library has decided that it will use the money to pay for subscriptions to electronic versions of journals. There are fifty such journals under consideration, and the price to sub- scribe to journal i for a year is pi, i = 1,...,50. Needless to say, LPi > 10,000, so not all these journals subscriptions can be purchased. To help decide what to choose, for each journal they have three pieces of informa- tion: c; is the number of times journal i is cited by articles in other journals, fi is the faculty's ranking of journals (higher is better), and qi is 1 if there's a nearby library which has either a print or electronic subscription to journal i, and is 0 otherwise. The budget can be taken as a system constraint. There are several ranked goals. In decreasing order of importance they are: (i) The average number of citations of the subscribed journals should exceed the average number of citations of all fifty journals. (ii) The average faculty ratings of the subscribed journals should exceed r. (iii) The number of subscriptions to journals which are already available in nearby libraries should not exceed n. (iv) The average number of citations of the subscribed journals which are not available in nearby libraries should exceed the average number of citations of all fifty journals by at least 20%. 4. (20 marks) After years and years of cuts to its budget, a university library has re- ceived an endowment which generates an annual income of $10,000. The library has decided that it will use the money to pay for subscriptions to electronic versions of journals. There are fifty such journals under consideration, and the price to sub- scribe to journal i for a year is pi, i = 1,...,50. Needless to say, LPi > 10,000, so not all these journals subscriptions can be purchased. To help decide what to choose, for each journal they have three pieces of informa- tion: c; is the number of times journal i is cited by articles in other journals, fi is the faculty's ranking of journals (higher is better), and qi is 1 if there's a nearby library which has either a print or electronic subscription to journal i, and is 0 otherwise. The budget can be taken as a system constraint. There are several ranked goals. In decreasing order of importance they are: (i) The average number of citations of the subscribed journals should exceed the average number of citations of all fifty journals. (ii) The average faculty ratings of the subscribed journals should exceed r. (iii) The number of subscriptions to journals which are already available in nearby libraries should not exceed n. (iv) The average number of citations of the subscribed journals which are not available in nearby libraries should exceed the average number of citations of all fifty journals by at least 20%