$(30$ marks$)$ A paper mill converts pulpwood $($Virginia$,$ White, and Loblolly pines$)$ to paper of low, medium and high grades. The pulpwood requirements for each paper grade, availability of each pulp$-$ wood, and selling price per unit are shown below. For example, the production of $1$ unit of low$-$grade paper requires $2$ tons of Virginia pine, $1$ ton of White pine and $1$ ton of Loblolly pine; the profit per unit of low$-$grade paper will be $$900.$ There are only $180$ tons of Virginia pine, $120$ tons of White pine, and $160$ tons of Loblolly pine available.