Bonus Question: (Note: You do NOT have to answer this part of the question, as it needs some mathematical background which is not part of the prerequisites nor the curriculum of this course, but if you do solve this problem, you will receive 3 extra points for this bonus question. After all, it is not hard to acquire the needed mathematical background by watching a lO-to20minute YouTube video on the Lagrangian Method of Constrained Optimization.) In the previous parts of the question, we investigated only 5 points on the curve, none of which was the "exact" optimal point for the economy to operate on. More precisely, one can use mathematical optimization methods to find "the" best or "the" optimal point on the PPC schedule, which is a single, unique point for any given set of values for a human life and for a job. Now, consider the average value of a human life to be $1,000,000 and the value of a saved job to be $60,000, as it was the case in the main context of the question. Here is the PPC curve and the exact equation of the curve that I have put together for you: '5 10 1011' {on} = no a) Using the above equation, solve for the exact optimal YL and Y J and report them below and make sure to put the units of each of the optimal values. (2 pts) b) Compute the maximized total monetarized benefit that this rational decision to be made by the government can bring about for the society/economy as a whole. (1 pt)