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Our goal in this paper is to determine whether a packaging machine of negligible width will fit through a hallway and into a certain room (see page 4 for comments about negligible width). Given the width of the hallway and the room, we apply calculus to find the minimum length available between the two. We determine that the machine will successfully fit into the room.doi:10.5038/2326-36184.108.40.206 fatcat:2sjpgj5aajafxopjapqvwsni4y