Why might Arauco want to own forests when they can buy lumber from the market?$2000$ logs of diameter $25$cm; or $1500$logs of diameter $38$cm; or $1000$ logs of diameter $50$cm; or a combination thereof. The kiln can dry up to $8920$ board$-$metres of lumber per week. $($a$)$ Formulate a linear model for this problem. $($b$)$ Solve the model using LINGO.