A university library is considering 15 journals as candidates for weeding out of their collection to yield annual subscription savings to meet a proposed budget cut. The citation counts CO, in the subject, and CRi in related area, of a journal Ji refer to the average number of times per year that articles appearing in J are referenced in the appropriate scientific literature. The faculty rating R of J is an average score between 1 and 5 given by the faculty of the university as an indication of the importance of journal J, in which the higher the score, the more important the journal is considered to be. The usage data u of J is the average number of times issues of journal Ji have been removed from the shelf for either borrowing or reading inside the library per quarter, obtained from data collected by the library. The availability rating a of journal J is an evaluation by the librarian on how easily available this journal is from other libraries; the smaller this rating the easier it is to obtain this journal from other sources. Corresponding data is given in Table 1. Journal Subscription ($/year) CO CRi Ri Ui ai J1 300 200 110 5 70 2 J2 220 50 120 5 70 1 J3 400 400 200 2 90 2 J4 700 60 80 4 90 2 J5 350 70 100 3 60 2 J6 260 160 210 5 90 3 J7 250 351 152 2 105 2 J8 360 130 111 1 85 2 J9 250 85 95 6 70 2 J10 210 70 65 5 40 3 J11 260 215 98 3 65 2 J12 320 45 35 4 45 1 J13 200 66 43 5 50 2 J14 520 130 120 4 70 3 J15 200 312 110 1 90 4 The following constraints have to be met. Table 1: Journals data Citation count in subject: Keep the average of the citation count in subject, per canceled journal, to < 250. Citation count in related area: Keep the average of the citation count in related area, per canceled journal, to 100. Faculty ratings: Keep the average of the faculty rating, per canceled journal, to 3. Journal usage: Keep the total usage rate per quarter, of all the journals canceled from this list, at 500 or less. Availability from other sources: Keep the average of the availability rating, per canceled journal, to