Question $3.(20$ points$)$ Ethan Steel, Inc. has three factories that manufacture steel components for three different rail projects located at three different sites. They want to determine how many steel components must be transported from each factory to each project site. The demand for the steel components for the three projects, A$,$ B$,$ and C$,$ are $2500,3000,$ and $4500,$ respectively. The production and shipping details are as follows:

Production details:

$\backslash$table$[[$Factory$,$Maximum capacity$],[1,3000],[2,5000],[3,3000]]$

Shipping details $($with per$-$unit shipping cost in dollars$)$:

$\backslash$table$[[,$Project$],[$Factory$,$A$,$B$,$C$],[1,7,8,2],[2,6,5,4],[3,1,9,6]]$

Develop a linear programming optimization model to determine the distribution plan $($from factories to projects$)$ that minimizes the total transportation cost. $($Do NOT solve the model.$)$