The board of trustees of Bilkent University wants to open up a number of coffee shops that would serve 8 different dormitories on campus. The board asks the helping hand of optimizing capabilities of IE 202 students to find the best shop locations. Preliminary studies have found 6 potential such locations and estimated the cost of opening a shop in cach such location. Depending on the location, the size of the shop might, differ and hence the opening costs differ. In particular, if a coffee shop is located at potential location 4 , students in dormitories 3,7 and 8 are close enough to buy their morning coffees from this shop and locating such a shop will cost Bilkent University $17,000. Extend your helping hand by providing integer models to each of the following demands of the board. a-) The board would like to know the minimum number of coffee shops to be opened to cover each dormitory. b-) Assume that the board has a mere budget of $75.000 and potential location j has and estimated Pj number of potential customers for j{1,,6}. This value is a given parameter and you might assume it is a lower value than the number of students residing in the dormitories that are covered by this location since some of Starbucks fanatics will not ever use these new national shops. The board would like to locate shops without exceeding its budget so that the number of students expected to get service is maximized. c-) Assume the board has no budget limitation in part b-) but would like to reach the highest. number of students with two shops. d-) The students demand that there should be at least two coffee shops within their reach so that they can escape from long lines if needed. The board would like to spend at most \$B dollars. (a given parameter) and guarantee that the number of students not having the second shop alternative is minimized. Note that every student should still be covered by at least one shop. Assume parameter Sj is the number of students residing in dorm j{1,,8}