Question: I need the Linear programming Formulation for the following problem (NOT SOLVE IT JUST NEED THE FORMULATION): I need to make a machinery part which

I need the Linear programming Formulation for the following problem (NOT SOLVE IT JUST NEED THE FORMULATION):

I need to make a machinery part which must to be processed from 4 cutting tools (A,B,C,D) which can move between points K (START) and L (FINISH).

The minimum time that the cutting tools need to move from K to L (and from L to K) is

A---1 Second

B-- 2 Seconds

C-- 5 Seconds

D-- 10 seconds.

Restrictions:

---I can have maximum two cutting tools simultaneously moving.

-- If there are two cutting tools moving then the direction must be the same for both of them and they must have the speed of the slowest tool

-- One of the tools (if there are two tools) [or the tool (if there is only one)], must carry an instrument to measure the distance . (Only one instrument is available) . Also this instrument checks if there is movement on the path KL (Situation "1" = I have movement, Situation "0" : there is no movement.

-- Time needed to transfer the instrument from one tool to another is negligible.

-- The cutting tools complete the process of the machinery part to the direction from K to L.

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