Question 2 12 marks You shouid be aide to answer this question after studying Unit 9. You can use Maxima to do the matrix arithmetic in this question, or you can do it by hand. If you use Maximo, then you do not need to include a printout or screenshot, but you must inciude sufcient details in your solution to make it clear what caicuiations Maxima has done. Two energy suppliers A and B supply electricity to three picturesque towns K, L, and M. During 2021: Town K received 20% of its electricity from supplier A and 80% of its electricity from supplier B. Town L received 30% of its electricity from supplier A and 70% of its electricity from supplier B. Town M received 35% of its electricity from supplier A and 65% of its electricity from supplier B. (a) (i) (ii) (iii) Draw a network diagram with input nodes K, L and M, and output nodes A and B, that represents the proportion of electricity each town received from its two energy suppliers. Write down the matrix that represents this network. Suppose that the total energy consumption in 2021 by towns K, L, and M are 1000, 1200, and 800 GWh respectively. Using the matrix that you found in part (a) (ii), determine the total energy generated by each power supplier in 2021. (Note: G'Wh = Gigawatt hours.) (b) Suppose that: Supplier A generates 40% of its electricity from renewable sources and 60% of its electricity from fossil sources. Supplier B generates 20% of its electricity from renewable sources and 80% of its electricity from fossil sources. Draw a network diagram with input nodes A and B, and output nodes R (Renewable) and F (Fossil) to represent the proportion of electricity each supplier generates from either a renewable or a fossil source. Find the single matrix that represents the network obtained by combining the network in part (a)(i) with the network above. (That is, the combined network represents the proportion of electricity each town K, L, and M received from either a renewable or a fossil source.) (iii) Which town has the highest percentage of electricity that comes from the renewable source, and what is the percentage? [2]