3. (25 marks) A university library has received an endowment which generates an annual income of $12,000. The library has decided that it will use all or some of this money to pay for new annual subscriptions to electronic versions of journals. There are six such journals under consideration. To help decide what to choose, for each journal they have three pieces of information: (i) For each journal they know the annual subscription cost in dollars. (ii) They know the number of times each journal is cited by articles in other jour- nals. (iii) Based on input from every faculty member, they know the average evaluations of the journals based on a scale from 0 to 10. Journal Annual Cost Citations Evaluations 1 $2900 150 8.2 23 2 $2300 135 7.7 3 $1800 140 9.8 4 $2600 190 9.3 5 $3200 128 8.3 6 $2400 155 7.6 The budget can be taken as a system constraint. There are three goals: (i) The number of unsubscribed journals should be as low as possible. (ii) The average number of citations of the subscribed journals should meet or exceed the average number of citations of all six journals. (iii) The average faculty evaluations of the subscribed journals should be at least (iii) The average faculty evaluations of the subscribed journals should be at least 8.1. The first goal is four times as important as the third goal, and the second goal is three times as important as the third goal.