Instruction: Please answer all the questions and include the necessary calculation process in your answer. Question 1 (20 marks) a. An entrepreneur is now deciding on investment and consumption for time 1 and time 2 in a free capital market. Explain the process of making an optimal decision with the aid of diagrams which including the transformation curve, market opportunities line, and indifference curve. (15 marks) b. An entrepreneur is having $500 as initial capital with two investment options available: Option 1: invest at a market interest rate of 10% Option 2: invest in an investment scheme that generates a return based on the transformation function of K = x, where K is the return at time 2 and x is the invested fund at time 1. Calculate the optimal fund should be allocated into these options at time 1. (5 marks)