9. Suppose we modify the production model in Section 1.3 to obtain the following mathematical model: Max 10x s.t. ax 40 I0 = where a is the number of hours of production time required for each unit produced. With = 3, a= 4,a= = 5, a=5, the optimal solution is x 8. If we have a stochastic model with a = or a 6 as the possible values for the number of hours required per unit, what is the optimal value for x? What problems does this stochastic model cause? Suppose I have got a solar-powered autonomous surface vessel somewhere in the fjords of Norway, supplied with a fairly recent set of maps, a GPS receiver, and no means of downlinking detailed commands from me. This vessel has to reach, say, the island of Hainan at the earliest possible moment. What are the deterministic algorithms for finding a maritime route on a globe? What is their time and memory complexity? Can I, for instance, use A* after transforming the map of the globe into a diagram with connected polygons (i.e. Delaunay triangulation on a sphere/ellipsoid) and what are other feasible approaches? Answers should ideally provide references to papers with discussion of the above-mentioned questions. As pointed out by Rob Lang, the algorithms must fit the usual criteria: in the absence of time constraints, lead to the shortest path between any two points on Earth's oceans and seas, or indicate pathfinding failure otherwise. There are interesting sub-topics here (trading pre-computation time/storage for online computations, providing slightly suboptimal routes before a deadline kicks in etc.), but these are ancillary to the main issue. Problem 1-09 (Algorithmic) Suppose the following is the mathematical model: Max 14x s.t. ax 65 X0 where a is the number of hours required for each unit produced. With a = 5, the optimal solution is x = 13.00. If we have a stochastic model with a = 3, a = 4, a = 5, or a = 6 as the possible values for the number of hours required per unit, what is the optimal value for x? Round your answers for the optimal solution to two decimal places. Round the answers for profit to the nearest dollar. If a = 3, x = and profit = $ If a = 4, x = and profit = $ If a = 5, x = and profit = $ If a = 6, x = and profit = $ What problems does this stochastic model cause? The problem with this stochastic model is certainty. and therefore the values of are not known with