2. A bank is in the process of developing a loan policy that involves a maximum loanable amount of $25 million. Let's assume each loan is valued at $50k. The following table provides important statistics about the types of loans, their interest rates, and their bad-debt ratio, i.e., the percentage of different types of loans that are defaulted upon. Defaulted loan means there is no profit, and the banks just receive its initial principle. In their current scheme, at least 40% of all loans must be either commercial or farm loans. Moreover, car loans should be at least 50% of all home, car, and personal loans, and bad debts should not be more than 5% of all loans. (a) Formalize the above as an optimization problem. State any assumptions made. [10 marks] (b) Write Julia code to solve the above problem. [7 marks]