Suppose you have 1720 meters of fencing available with which to build three adjacent rectangular corrals as shown in the figure. Find the dimensions so that the total enclosed area is as large as possible. The smaller side is C] meters The longer side is l:] meters You need to construct an open-top rectangular box with a square base that must hold a volume of exactly 275 cm3. The material for the base of the box costs 4 cents/cm2 and the material for the sides of the box costs 5 cents/cmz. The dimensions for a box that will minimize the cost of the materials used to construct box are: Consider a rectangle inscribed in a right triangle with sides A = 9 and B = 27. We want to determine the dimensions of the rectangle with largest area that can be inscribed inside the triangle. A B .y x ll A The area of the rectangle, as a function of a: and y is A=C1 Use the substitution principle to rewrite the area as a function of m. (Hint: Similar Triangles) A=A(m)=:] Then A'(:l:) = C] To determine optimal values, we need to look at A ' (at) = 0. Solving for :L' and, ultimately for 3;, yields inches = f inchesA cylinder shaped can needs to be constructed to hold 500 cubic centimeters of soup. The material for the sides of the can costs 0.02 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.05 cents per square centimeter. Find the dimensions for the can that will minimize production cost. To minimize the cost of the can: Radius of the can: A fence 6 feet tall runs parallel to a tall building at a distance of 2 ft from the building as shown in the diagram. LADDE 6ft 2ft 9 q We wish to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. [A] First, find a formula for the length of the ladder in terms of 9. (Hint: split the ladder into 2 parts.) Type theta for 6. w: [B] Now, find the derivative, L'(0). Type theta for 6. W: [C] Once you find the value of 9 that makes L '(9) = 0, substitute that into your original function to find the length of the shortest ladder. (Give your answer accurate to 5 decimal places.) mew:1feet