A rectangular box is to be made from a piece of cardboard 25 inches long and 10 inches wide by cutting out identical squares from the four corners and turning up the sides, as in Figure 1 (Section 3.4, Example 1). Find the dimensions of the box of maximum volume. Length: inches, width: inches, height: inches. What is this volume? cubic inches A farmer has 400 meters of wire fence with which he plans to build two identical adjacent pens, as shown in Figure 3 (Section 3.4, Example 2). What is the maximum area of such an enclosure? square meters A right circular cylinder is inscribed in a right circular cone with altitude 10 and radius of the base 6. What is the greatest possible volume of the cylinder? See Example 3 page 168 for a picture and a similar example. The top and bottom margins of a poster are 2 cm and the side margins are each 2 cm. If the area of printed material on the poster is fixed at 390 square centimeters, find the dimensions of the poster with the smallest area. Width = Height = The manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 324 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 1 dollar increase in rent. Similarly, one additional unit will be occupied for each 1 dollar decrease in rent. What rent should the manager charge to maximize revenue? Note: Revenue is the total amount of money brought in; in this problem it is equal to the rent per apartment times the number of apartments rented