PROBLEM $2$: FORMULATION $(20$ points$)$The Windsor Glass Company is planning to launch two new products. Product $1$ is an $8-$foot glass door with aluminum framing and Product $2$ a $4$x$6$ foot double$-$hung wood$-$framed window. Aluminum frames are made in Plant $1,$ wood frames are made in Plant $2,$ and Plant $3$ produces the glass and assembles the products. Product $1$ requires some of the production capacity in Plants $1$ and $3,$ but none in Plant $2.$ Product $2$ needs only Plants $2$ and $3.$ The marketing division has concluded that the company could sell as much of either product as could be processed by these plants. The management ofthe company wants to determine what mixture of both products would be the most profitable. The following table provides the information available. Production time per batch, hoursProduction time available per week,hours Product Plant $1211062051232413$Profit per batch $$2,000$ $$5,000$a$)$ Formulate the problem as LP$.(10$ points$)$b$)$ Solve the problem using Graphical Solution method. $(10$ points$)$