1. Simulation Optimization. A taxi driver in the city of New York wants to decide how much time he should work per day,r to maximize his income. Assume that the average money per ride isp dollars. The number of trips he could fulll depends, of course, on how much time he works. If he works fort hours, the number of dispatches D he gets is a Poisson random variable with meann) = log(1 +t). In other words (as expected), the longer he works the more (on average) rides he gets. Also, the cost (fuel, car depreciation, etc) of working increases as the working timet increases. Let us assume here that there is a cost of 95: for working per hour (half an cur costs 131181le2 etc). If he chooses to work 3 hours, the total operating cost is 3:. (a) Let p = 12, c = 3. Assume the driver only works for an integer number of hours, and can not work more than 10 hours a day. Design and code a simulation based algorithm to nd the amount of time he should work in order to maximize his expected net income. Of course, once you have such a code you could have much more general specifications (cost need not be linear, dispatches could follow an arbitrary structure etc.). The reason for this specific stucture we used is that now we can compare yOur simualtiOn result to (b) Analytically derive the optimal amount of time a driver should work if he wishes to maximize hisf' her expected income? How does this compare to your answer to part (a)