3.3 O llmlzatlon Problems 9. A north-south road intersects an east-west road at a point 0 . A motorcycle crosses 0 . at noon. travelling West at a constant speed of 80 krm'h . At the same time. a car is 501:: South of 0 . travelling North at 60 km!!! . Find the time at which they are closest to each other. and approximate the minimum distance between them. 10. The sum of two non-negative numbers is 16 . Find the maximum possible value and the minimum possible value of the sum of their cube roots. 3.3 Optimization Problems 7. A box with an open top is to be constructed from a rectangular piece of cardboard, 2m by 3m , by cutting out a square from each of the four corners and bending up the sides. Find the dimensions of the box corresponding to a maximum volume 8. Find the dimensions of the largest right-cylinder that can be inscribed in a cone of radius R = 6m and height H =9m .3.4 Optimization Problems In Economics and Science 1. A farmer wants to fence an area of 9600m2 in a rectangular field and divide it in half with a fence parallel to one of the sides of the rectangle. Find the dimensions (length and width} of the rectangular field that minimize the cost of the fence? 2. The selling price (in $} of an item is p(x) =600.02x , where x is the number of items sold per day. If the cost {in $} of manufacturing x items is 60:) = 1000+ 10x, nd the number of items to be manufactured per day in order to maximize the profit