P C: imiz In The rm is 1resinr interested in maximizing prbts. Its prot model is given by the function: f(x) = Tsimc where it represents the number at new subscribers per year in thuusands. Determine how many new subscribers are needed to maximize prbt given that the number bf subscribers supported has to be between 5000 and 1U? [5] Fag E: Veggrg MindBook decides to diversify their portfolio and invest in the \"Robolvlap\" technology which is a robot that maps different types of ten'itories. The new CEO is trying to make some drastic changes to some of the software and hardware systems in the new version of the robot. You have been hired by the opposing faction in the hoard to lead an investigation on how the performance of the robot is affected by the new proposed changes. [3] a] The rst system that you will test is the navigation system. The robot maps the territory by calculating distances and angles whilst moving between various locations. it then stores on its system the shortest direct path from initial location to the intended target. During the test the robot navigates around a muddy surface in the following path: 55cm [NW] and then moves 45cm [sso'iw]. The robot sends back to the server the following overall shortest path: i'cm ['W1El\"S]. Lise triangle or parallelogram method to verify the precision of the mbot's navigation system. Diagram not to scale b] The next test involves the performance of the new battery. The robot encounters an obstacle on his journey. Using its arm it applies a force of 3511 at an angle of 25" below horizontal and is able to displace the object for 20m in a time of E5s. At the beginning of the test the battery's is displaying a total stored energy {abilityr to perform mechanical work} of 2500 him. What would be the remaining energy displayed at the end of the test? Useful formula: as = w [change in available energy is equal to the work done} c} The robot is also able to lift itself by pushing its arm against the ground in a rotational motion around an axis at the back wheel. This is useful to move on top of obstacles encountered during exploration. The robot applies a force [10.5.15] at a point where the arm vector is [-53.3]. Determine the torque vector. Diagram for ilusbslion erposas only d] One exploratoryr mapping session for a 1m by 1m can last 5 minutes. The new mapping system should be able to handle absolute coordinates in space as well. That is the compass directions might not be available. This mapping system uses cartesian system using as origin {c.co) the landing site. The robot starts the exploration at the point (1, 2. -3,'I and ends the exploration at the point [2. c, 1}. Describe the trsjectorzlr of the move using the equation of line between the starting and the nal location of the robot. Diagram for Ilustratlm purposes onlyI I iIiIIJN-Jln 3 Emit. '1' .u
