PART 1: MAXIMISING A FUNCTION (15%) Objective: Find the maximum value of / (x, y, 2), where /(x,y. =) = exin(liz) + cin(10n) + sin(20es) + sin|70sin(x)] - sin(30 cos(=)] + sinsin(30y)| -sin|10(x + y)| + + +22 ti Constraints: The solution must be subject to the (hard) constraints: and I, M. ZER You should explain the approach taken, attaching any programming code that is usexl - provide comments to the code where appropriate. PART 2: MULTI-OBJECTIVE OPTIMISATION (25%) An investment firm has 150000 to invest and has 100 possible options to choose from. The option number i (column 1), expected return s, (column 2), and investment required (column 3) for each option are given in the file Part2. txt (on Canvas)- (i) Single Objective: Assuming the investment firm has a single objective, to maximise their total expected return, /, defined as solve this optimisation problem - here r, is a binary value denoting the investment in op- tion i or not. Give the list of options they should invest in and their total expected return, ensuring that E GI, $ 50000. (ii) Multi-objective: Now assume the decision maker has two objectives: to maximise the total expected return, /, but also to minimise the total number of invest- ments they make, 2, defined as Investigate the possible choices the firm could make in this situation. In both parts, you should explain the approach taken, attaching any programming code that is used - provide comments to the code where appropriate