1. You are working for Yarra Valley Water as a data scientist and decide to use a polynomial of degree :1? that is, HI} = 41.11\" + ear3 + m5 + a1: + on? to model the daily water usage of a Melbourniau family at time I for all I such that 12 i: I 5 1'2. 1]: = 12 and I = 1'2 correspond to 3am so may = 1112}. We also also assume that Sam and 9pm {I = E and z = 6, respectively} are local maxima of the usage. in this question we assume that the total 1water consumption during the day equals 24. {a} Write a linear system of equations describing the following properties: [4] ['1] ff12l= iii-12L [ii] I = 43,13 are stationary points of 3", {iii} the total water consumption is 24. {b} Using Gaussian elimination... nd all solutions of the linear system obtained in {a}. [4] {c} Find all functions j that satisfy all of the data given in the description of the question. ['F] {d} is it possible that the total water consumed during the night hours from 1am to 5am [3] is smaller than 2 {that is the average over these four hours is less than half of the daily ave rage} 5' If your unsure-r 1's F'yes'J than you. should gene on. Hompfe of such function f fmm {c}; othemrise justify why it is not possible