Question 5 This question is worth 30 marks. a. A Korean Seniors Luncheon Club in Milton Keynes recently looked at two options for transporting members to the club and then home after lunch. Ezee Cabs quoted a flat fee of 120 per week, while Class Motors wanted an upfront payment of 300 and then a flat fee of 90 per week. Using the concept of a break-even chart, determine which of the two options is more economical, and after which point it becomes so. (In other words, which option will be of lower cost in the longer term. Consider a period of four months in your deliberations, and detemine whether a point is reached where one option becomes cheaper than the other) (10 marks) b. A window frame is shown in Figure 1 below. The thickness of the frame and the struts within the frame are small compared to the other dimensions, and do not need to be accounted for separately. Figure 1 A window made up of six glass panes i. If 9 metres of frame are available to go around the outside perimeter of the window, (9-2h)/6 Explain each step of your working. show that w (4 marks) ii. Show that the area of the window, A, can be expressed in terms of h by the quadratic equation: A 4.5h-h2 Explain each step of your working. (4 marks) i. Using the method described in Section 11.3 of the Part 3 book, find the overall dimensions of the frame (the height and width of the window) that make the area of the window a maximum. Explain each step of your working. (4 marks) iv. Using a spreadsheet, plot a graph showing the area of the window, A, as a function of h. Paste a copy of the graph into your TMA. (6 marks) Using the height and width of the window you found in part (ii) above, calculate the maximum area of the window. Compare this with the value shown in the graph you produced for part (iv) of this question. V (2 marks)