1. Optimization Joe has a fierce argument with Cheryl on a lakeshore. He grabs her backpack, runs 16 miles away from her along the lakeshore, then throws it directly* into the lake. So now the backpack is 5 miles away directly from Joe. * directly = in a direction that is perpendicular to the lakeshore Cheryl can run at 6 miles per hour along the lakeshore and then dive into the lake and swim at a speed of 4 miles per hour to save her backpack before it sinks into the lake. (Assuming that the backpack is still floating on the water and does not move/sink until Cheryl gets there) a)d) What is the shortest time (in minutes and seconds) Cheryl can take to save the backpack? ble) How far should Cheryl run along the lakeshore until she dives into the lake and start swimming directly toward her backpack in order to minimize the time to save it? c)f) What is the maximum time (in min. and sec.) that Cheryl can take to save her backpack? wollot arif to agy! class to. Lasal fio abuboi drum upY Grading Scheme neilnut bumbaup 6 lo nodermolar Part (a) /15A Part (b) /2A Part (c) /3A Generic Optimization Checklist: Ensure you have all components to achieve full marks Drawing of a fully-labelled image that represents the given optimization scenario All related variables/functions defined Algebraic steps are clear and thorough 0 Justification included regarding whether the critical point represents a maximum or minimum (local or absolute?) 0 Final conclusion statement