Three towns, A, B, and C receive electricity from two suppliers, X and Y . During 2023: Town A received 90% of its electricity from supplier X and 10% of its electricity from supplier Y . Town B received 15% of its electricity from supplier X and 85% of its electricity from supplier Y . Town C received 55% of its electricity from supplier X and 45% of its electricity from supplier Y . (a) (i) Draw a network diagram with input nodes A, B and C, and output nodes X and Y, that represents the proportion of electricity each town received from its two energy suppliers. (ii) Write down the matrix that represents this network. (iii) Suppose that the total energy consumption in 2023 by towns A, B, and C are 700, 900, and 800 Gigawatt hours (GWh) respectively. Using the matrix that you found in part (a)(ii), determine the total energy generated by each power supplier in 2023. (b) Suppose that: Supplier X generates 20% of its electricity from renewable sources and 80% of its electricity from fossil sources. Supplier Y generates 60% of its electricity from renewable sources and 40% of its electricity from fossil sources. (i) Write down the matrix that represents the proportion of electricity each supplier generates from either a renewable or a fossil source. (ii) Hence find the single matrix that represents the proportion of electricity each town A, B, and C received from either a renewable or a fossil source