AP Calculus Unit 5 5.4a Optimization Problems Please show your work 1. A bicycle manufacturing company has determined that the total cost of producing an bike is given by the equation, 6' = 8x2 1%): + 1800, where XiS the number of bicycles per minute the company makes. How many bikes should the company manufacture per minute to minimize the cost? 2. Elon Musk res a rocket into the air. and its height in meters at any given time, r, can be calculated using the formula ME) = 1600 + 196t 4.9!:2. Find the maximum height of Elon's rocket and the time at which the rocket reaches that height. 3. A swimmer is at a point 500 meters from the closest point on a straight shoreline. She needs to reach a cottage locate 1,300 meters down shore from the closest point. If she swims at 4 mils and walks at 6 mls, how far from the cottage should she come ashore so as to arrive at the cottage in the shortest time? 4. A 384-square-meter plot of land is to be enclosed by a fence and divided into two equal parts by another fence parallel to one pair of sides. What dimensions of the outer rectangle will minimize the amount offence used? Source: AP Calculus, Princeton Review