1. Manuel, Marcel, and Michelle are enjoying their TAOR project so much that they want to take a photo with their devoted advisor, Miguel, so that they will be able to remember these good times for evermore. Miguel, committed as always, kindly agrees and they set up in a row facing the camera. Manuel, Marcel, and Miguel each have shoulder-to-shoulder lengths of 60cm. Michelle prefers to stand side-on for the photo and so takes up a horizontal space of 40cm. They are all keen to be as close to each other as possible but Marcel smells a bit (and didn't really pull his weight in the project). Therefore they silently agree that the emotional cost (measured in tears of longing) of each centimetre separating Manuel, Michelle, and Miguel is 5 and the cost of each centimetre between Marcel and the others is 1. All of the students express how they would also prefer it, given the choice between arrangements of equal emotional cost, if their beloved project supervisor were situated towards the centre of their photo. Michelle pipes up that, in an act of devotion, she will always face Miguel and, if also given the choice between two arrangements, she would much prefer to face to her left (her right side is her best side). [NOTE: Due to the importance of this photo, they have been given the go-ahead from Nicola Sturgeon to not have to adhere to any social distancing. Therefore they may pose side by side if they choose to.] (a) [7 marks] Viewing this as a single-row layout problem, use logic and enumeration (by hand) to determine the optimal arrangement, from left to right, of Manuel, Marcel, Michelle, and Miguel and the emotional cost of this arrangement. Justify your answer fully. Using what is provided in the question, include a little artist's impression of this perfect photo. Tom, envious of the attention Miguel is getting, jumps in and forces himself into the photo. In an embarrassing and desperate attempt to seem 'down with the kids', he poses, reclining on the floor at the group's feet, taking up 190cm of space. Manuel, Marcel, Michelle, and Miguel grudgingly agree to take another photo, and they can remain standing or crouch to join Tom at their feet. They are all indifferent to Tom's presence so there is no emotional cost associated with their distance from Tom. Zoom- ing out as far as the camera can in order to fit in those standing and lying/crouching down, the frame of the photo can now only fit a width of 240cm. 1 (b) [5 marks) Viewing this now as a double-row layout problem, use logic and enu- meration (by hand) to determine the optimal arrangement of Manuel, Marcel, Michelle, Miguel, and Tom, and the emotional cost of this arrangement. Justify your answer fully. Again, include a little artist's impression of this photo. 1. Manuel, Marcel, and Michelle are enjoying their TAOR project so much that they want to take a photo with their devoted advisor, Miguel, so that they will be able to remember these good times for evermore. Miguel, committed as always, kindly agrees and they set up in a row facing the camera. Manuel, Marcel, and Miguel each have shoulder-to-shoulder lengths of 60cm. Michelle prefers to stand side-on for the photo and so takes up a horizontal space of 40cm. They are all keen to be as close to each other as possible but Marcel smells a bit (and didn't really pull his weight in the project). Therefore they silently agree that the emotional cost (measured in tears of longing) of each centimetre separating Manuel, Michelle, and Miguel is 5 and the cost of each centimetre between Marcel and the others is 1. All of the students express how they would also prefer it, given the choice between arrangements of equal emotional cost, if their beloved project supervisor were situated towards the centre of their photo. Michelle pipes up that, in an act of devotion, she will always face Miguel and, if also given the choice between two arrangements, she would much prefer to face to her left (her right side is her best side). [NOTE: Due to the importance of this photo, they have been given the go-ahead from Nicola Sturgeon to not have to adhere to any social distancing. Therefore they may pose side by side if they choose to.] (a) [7 marks] Viewing this as a single-row layout problem, use logic and enumeration (by hand) to determine the optimal arrangement, from left to right, of Manuel, Marcel, Michelle, and Miguel and the emotional cost of this arrangement. Justify your answer fully. Using what is provided in the question, include a little artist's impression of this perfect photo. Tom, envious of the attention Miguel is getting, jumps in and forces himself into the photo. In an embarrassing and desperate attempt to seem 'down with the kids', he poses, reclining on the floor at the group's feet, taking up 190cm of space. Manuel, Marcel, Michelle, and Miguel grudgingly agree to take another photo, and they can remain standing or crouch to join Tom at their feet. They are all indifferent to Tom's presence so there is no emotional cost associated with their distance from Tom. Zoom- ing out as far as the camera can in order to fit in those standing and lying/crouching down, the frame of the photo can now only fit a width of 240cm. 1 (b) [5 marks) Viewing this now as a double-row layout problem, use logic and enu- meration (by hand) to determine the optimal arrangement of Manuel, Marcel, Michelle, Miguel, and Tom, and the emotional cost of this arrangement. Justify your answer fully. Again, include a little artist's impression of this photo