Bastille College Is Going to Purchase New Computers for Both

Bastille College is going to purchase new computers for both faculty and staff.There are a total of 50 people who need new machines - 30 faculty and 20 staff.The cost of the basic personal computer with monitor and disk drive is $2,000, while the deluxe version with VGA and advanced processor is $3,500.Due to internal politics, the number of deluxe computers assigned to staff must be less than half the number of deluxe computers assigned to faculty.The College feels that it must purchase at least 5 deluxe computers for the faculty; if possible, it would like to purchase as many as 20 deluxe computers for the faculty.Staff members do feel somewhat "put upon" by having a limit placed upon the number of deluxe machines purchased for their use, so the College would like to purchase as many deluxe machines for the staff as possible (up to 10).The budget is $100,000.Develop a goal programming formulation of this problem that treats each of the requirements stated above as an equally weighted goal.