The Whitt Window Company is a company with only three employees which makes two different kinds of hand$-$crafted windows: a wood$-$framed and an aluminum$-$framed window. They earn $$180$ profit for each wood$-$framed window and $$90$ profit for each aluminum$-$framed window. Doug makes the wood frames and can make $6$ per day. Linda makes the aluminum frames and can make $4$ per day. Bob forms and cuts the glass and can make $48$ square feet of glass per day. Each wood$-$framed window uses $6$ square feet of glass and each aluminum$-$framed window uses $8$ square feet of glass. The company wishes to determine how many windows of each type to produce per day to maximize total profit. Please answer below questions:$($a$)$ Describe the Wyndor Glass Co$.$ problems. Construct and fill in a table for this problem, identifying both the activities and the resources.$($b$)$ Formulate a linear programming model for this problem. Describe the objective functions and constraints.$($c$)$ Use the graphical method to solve this model.$($d$)$ A new competitor in town has started making wood$-$framed windows as well. This may force the company to lower the price they charge and so lower the profit made for each woodframed window. How would the optimal solution change $($if at all$)$ if the profit per wood$-$framed window decreases from $$180$ to $$120?$ From $$180$ to $$60?($You may find it helpful to use the Graphical Analysis and Sensitivity Analysis procedure$).($e$)$ Doug is considering lowering his working hours, which would decrease the number of wood frames he makes per day. How would the optimal solution change if he makes only $5$ wood frames per day? $($You may find it helpful to use the Graphical Analysis and Sensitivity Analysis procedure$)$