a. Question 5a is worth 10 marks. An international NGO (Non-Governmental Organisation) is keen on setting up power supplies for remote communities in Kenya and calls for bids from local engineering firms. Two submissions are received: Kendalla quote 8000 KES* a week, but with a one-off signing-up fee of 50000 KES, whilst Quesiko quote 15000 KES per week. [*Please use the local currency (Kenyan shilling - KES)] i. Using a graphical method, determine the time (to the nearest week) at which the cost for using both companies is the same. ii. Then, state which company would be more economical to use for the project, if it is to go beyond the point determined in (i). (10 marks) b. Question 5b is worth 20 marks 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. h y Figure 1 A window frame made up of eight equal rectangles. Not drawn to scale. Hide description The diagram shows a window frame made up of eight identical sized rectangles. The window frame measures two rectangles wide by four rectangles high. The height of each rectangle is labelled as 'h' and the width as 'y'. i. If 18 metres of frame are used to go around the outside perimeter of the window, show that: y = (9-4h)/2 Explain each step of your working. (4 marks) ii. Show that the area of the window, A, can be expressed in terms of h by the quadratic equation: A = 36h - 16h Explain each step of your working. (4 marks) iii. 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) v. Using the height and width of the window you found in Part 3 above, calculate the maximum area of the window. Compare this with the value shown in the graph you produced in Part 4 of this Question. (2 marks)