(5 points) You and your family are going on a cross-country road trip. You know the route you will be taking. There are n hotels along this route. You know the location and rate r; for each hotel h; along the route, for 1 sjan.? You also know the distance d; of each hotel from your starting point. You will eventually reach your destination, after traveling a total distance D. You can travel a maximum of m miles in a day. Your goal is to minimize the total cost of lodging on your trip of distance D. Let's call this total cost roomCost(D). Using the following steps, write an equation for the recursive solution to this problem. a) Will you necessarily minimize the number of nights you spend on the road in order to minimize the overall hotel cost? b) There will be some hotel h; that is the last hotel you will stop at before your destination. Not all hotels are candidates to be this last hotel. What inequality relates the distance d; from the starting point to this last hotel, and the distance D? c) Given that you stop for the last night at hotel hj, at a distance dj from your starting point, for a cost of rj, what is the recursive equation for the total room cost for all the previous nights (if any)? This will be of the form roomCost(D) = d) What is the recursive equation for minimizing the overall cost roomCost(D)? In other words, take the equation in part c and minimize it over the appropriate variable(s)