Structuring the Sell$-$or$-$Process$-$Further Decision

Jack's Lumber Yard receives $8,000$ large trees each period that it subsequently processes into rough logs by stripping off the tree bark and leaves. Jack's then must decide whether to sell its rough logs $($for use in log cabin construction$)$ at split$-$off or to process them further into refined lumber $($for use in regular construction framing$).$ Jack's normally sells logs for a per$-$unit price of $$500.$ Alternately, each log can be processed further into $800$ board feet of lumber at an additional cost of $$0\mathrm{.}05$ per board foot. Also, lumber can be sold for $$0\mathrm{.}75$ per board foot. $($Note: One tree is equal to one rough log$.)$