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:

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

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.$)$