Formulate this problem as an LP (do not solve, just formulate please) There are currently 3 machines in a factory: P1, P2, and P3. Assume that this rectilinear shaped factory is located on the first...

Formulate this problem as an LP (do not solve, just formulate please)

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 to 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.
You can check the provided links below to see how overhead cranes work. Crane
movement consumes both time and energy. Therefore, minimizing the total
movement time is the main goal.
The problem is to determine the coordinates of the new machines that will minimize
the total movement time.
Vinçleri çalışırken görmek için:
http://www.youtube.com/watch?v=GZZrelz-iZk
https://www.youtube.com/watch?v=P_1MuAhO6kY&ab_channel=AhmedAwad