Answered: There are currently 3 machines in a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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formulate this probblem.

There are currently 3 machines in a factory: P1, P2, and P3. Assume that this rectilinear shaped factory is located on the first quadrant of the coordinate system and one corner is at the origin (point (0,0)). The coordinates of the existing machines are as follows: P1=(10,15), P2=(20,25) ve P3=(40,5) To meet the increasing demand and respond to changing customer demands, the company decided to grow and acquired two new machines: N1 and N2. When these two machines are put into operation, they will exchange materials with each other and with the other three machines. 400 units of material will be transported between the 2 two new machines in a week. Similarly, 400 units will be transported between N1 and P1, 0 between N1 and P2, and 500 units between N1 and P3. The transportation between N2 and P1, P2, and P3 are 200, 100, and 0, respectively. Materials are transported with an overhead crane. This crane can move linearly in x and y coordinates and can move simultaneously in both directions. It moves at a speed of 0.8 m/sec on the x-axis, its movement on the y-axis occurs at a speed of 1 m/sec. While the crane moves from one point to another, it starts to move in both x and y directions at the same time. As soon as one of the coordinates reaches the coordinate of the destination point, the movement in that direction is terminated. But its motion in the other direction continues until it reaches the coordinate point on that axis also. Crane movement consumes both time and energy. Therefore, minimizing the total movement time is the main goal

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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