The corner of a corridor at a building is made up of a 7-ft wide walkway and a 5-ft wide walkway as shown in the diagram. Pallets are frequently 5 ft wheeled around this corner. Determine the maximum size (i.e., area) of the pallet having width w and length / that can pass through this corner. Note: The derivatives needed to construct the system of equations to find the critical values are a bit overwhelming and intimidating. They are not difficult but can be tedious. You may use technology to determine the derivatives. 7 ft In addition, you will see that the system of equations will be quite unpleasant to solve manually. You can approximate the solutions to within 0.10-ft.1I"ou are constructing a Iwater channel with flatbottom and the 2 side walls angled up as shown. A 21-inch Imidi: trench {W = 24}is dugged out and the walls are then constructed. See the diagrams for the details of the geometry. Cine 1allay of imagining the construction is to take a piece of paper and then bend up 2 equaHength x of the ends through the same angle 3' to form the channel. Determine the length I and the bend angle 3 to give the mayimnm cg; sectional area for the channel to obtain the largest water ow. Note: The system of equation that you end up with is highly nonlinea r. It can be solved by hand but its UK it you approximate the solution