A university library has received an endowment which generates an annual income of $10,000. 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 five 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 journals, and (iii) they know the average faculty member's evaluations of journals based on a scale of 0 to 10. Journal 1 2 3 4 5 Annual Cost Citations Evaluations 135 7.6 130 9.9 200 98 146 $2300 $1900 $1600 $3400 $2500 9.2 8.1 7.8 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 five journals. (iii) The average faculty evaluations of the subscribed journals should be at least 8. The first goal is five times as important as the third goal, and the second goal is twice as important as the third goal. (a) In LINGO syntax or as an Excel file, define the set of decision variables and the three deviational variables. write the three sets of deviational constraints, and complete the model with an objective function and the budget constraint. (Hint: For two of the deviational constraints, you will need to cross-multiply before inserting the deviational variable. You might want to try this by hand before entering it into a computer.) (b) Solve the model in LINGO or the Excel Solver, and state the recommended solution.