A handcrafted window company with only three employees makes two kinds of windows: wood-framed and aluminium-framed windows. The company earns 60 profit for each wood-framed window and 30 profit for each aluminium-framed window. The company wishes to determine how many windows of each type to produce per day to maximise total profit [Note that some windows can be partly completed]. Dan is a wood specialist and can make 6 wood-framed windows each day. Sarah makes the aluminium frames and can make 4 per day. The third employee, Mike, forms and cuts the glass required for both kinds of frames. 48 square feet of glass are available each day for glasswork. While the wood-framed window uses 6 square feet of glass, each aluminium-framed window uses 8 square feet of glass. Additionally, from historic data, the number of aluminium-framed windows produced should not be more than two times the number of wood-framed windows produced. Finally, a breakeven analysis previously conducted on the companys operations indicates that at least three windows must be produced each day. a. Formulate a linear programming model for this problem. [15 marks] b. Solve this problem graphically. [50 marks] c. A new competitor who makes wood-framed windows is in town. The company is exploring whether it can respond to this by lowering the price of its woodframed windows by cutting its profits. How would the optimal solution change (if at all) if the profit per wood-framed window decreases from 60 to 40? From 60 to 20? [25 marks] d. Sarah is considering increasing working hours, which would increase the number of aluminium frames made per day. How would the optimal solution change if Sarah makes 5 aluminium frames per day [10 marks]