Companies A$,$ B$,$ and C supply components to three plants $($F$,$ G$,$ and H$)$ via two crossdocking facilities $($D and E$).$ It costs $$4$ to ship from D regardless of final destination and S$3$ to ship to I regardless of supplier. Shipping to D from A$,$ B$,$ and C costs $$3,$ $$4,$ and $$5,$ respectively, and shipping from E to F$,$ G$,$ and H costs $$10,$ $$9,$ and $58,$ respectively. Suppliers A$,$ B$,$ and C can provide $200,300$ and $400$ units respectively and plants F$,$ G$,$ and H need $350,350,$ and $200$ units respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice.

Formulate the full LP model for this problem.