A rover needs to travel along a trajectory with steep ascents and descents. It uses batteries as a source of energy. When the rover goes down, the battery recharges and when it goes up, it consumes energy from the battery. When the battery is empty (level is zero) the rover cannot go up. We assume that ascending one meter consumes one unit of energy (level decreases by one unit); descending one meter recharges the battery with one half a unit of energy (level goes up by 0.5 unit). A trajectory is given by a finite sequence of integers: for instance, the sequence s- (-2,3, -4,5,-2,1) corresponds to a trajectory of size 6, with 6 ascents/descents, where the rover has to descend 2 meters, ascend 3 meters, descend 4 meters, ascend 5 meters, descend 2 meters and ascend 1 meter. Trajectories can be of arbitrary but finite sizes The battery also has a maximum capacity C0. (Note: the maximum capacity is not a constant but an input of the problem.) We want to determine the minimum initial level with maximum capacity of the battery to be able to complete a trajectory, such that when the trajectory is completed, the battery level is at least m (a positive integer) Question 5 Consider the example trajectory s from the problem statement. What is the minimum initial level with maximum capacity for this trajectory, if m5 and C 10000? Question 6 Give an example with a trajectory of size 4 that admits a solution. (The example should include both the sample trajectory and values C and m.) Question 7 Give an example with a trajectory of size 4 that does not have a solution. (The example should include both the sample trajectory and values C and m.) Question 8 Consider again the example trajectory from the problem statement, and extend it by two further moves (i.e. s'- (-2,3, -4,5,-2,1, s7, ss)). What condition(s) have to hold between the various quantities (e.g. s7, ss, C, m)? Your answer should be in the form of one or more equations or inequalities. Question 9 Give a formal statement of the minimum initial level with maximum ca- pacity problem. The formal statement should include the input and output for the problem, where the output specification should contain one or more equations or in- ualities relating the various problem quantities Question 10 Propose an algorithm to solve the minimum initial level with maximum capacity