I am trying to learn Linear Programming. However, I don’t know how to solve the following problem. Maybe you can help, because I am curious to the right approach and solution for this problem. It involves Newtonian mechanics.
A company uses a crane for lifting (see picture). The crane has $2$ hoists. They can work at the same time. Both ends can take $10000 \,\rm N$. If the two hoist both pick 1 artefact at the same time, what is the maximum force that the first hoist can take?
The force on hoist $1$ is represented by $x$.
The force on hoist $2$ is $9000 \,\rm N$.
The position of hoist $1$ is fixed.
The position of hoist $2$ is not fixed, as long as it is to the right of the first hoist.
The distance between both hoist is represented by $y$.