OPTIMIZATION WORKSHEET I 1. A rectangular fence is to be built on the side of Sally’s house to create a garden. The side of Sally’s house will be used for one side of the garden. If Sally has 100 f t of fencing, what dimensions will maximize her garden’s area? 2. A rectangular box is to be made from a piece of 10 in by 20 in piece of cardboard by cutting out squares from the edges and gluing them together. What dimensions will maximize the volume of the box? 3. Find two positive real numbers x and y such that their sum is 50 and their product is as large as possible. 4. A rectangle of fixed perimeter 36 cm is rotated around one of its sides, thus sweeping out a figure in the shape of a right circular cylinder. What is the maximum possible volume of that cylinder? 5. Find the largest possible value √ of s = 2x + y if x and y are side lenghts in a right triangle whose hypotenuse is 5 units long. 6. What is the smallest perimeter possible for a rectangle whose area is 16 in2 ?