Name: Gisselle Washington Optimization problems Date: Oct. 23, z01q Period: 1 Prove Show that of all the rectangles with a given area, the one with the smallest perimeter is a square. hMimimun 1et A be a given 100f area 100 = Lw Suppose a cylindrical can is being made to hold 1 liter of oil. Design the can so that the minimum amount of metal can be used. The area of the metal is given by ar+2rh Note that 1L 1000cc so ar h = 1000, h 1000 1 2

Exc 2.5 Q19 needed to be solved correctly

1. A can manufacturing company is designing a can of cat food to hold (have a volume 200cm³. They have written out that the equation for the surface area for a can with th volume is S = 277² +200. Explain why the equation is wrong and how to fix it. F2 Useful Formulas: • V = πr² h • S=2πr² + 2πrh Edit View Insert Format Insert Format Tools Table 12pt 4 F3 Paragraph O E 1 4⁰) $ F4 -2 BIUAv2v T²v DII F5 DI E F6 * F7 & PrtScn : F8 Home F9 End F1

A piece of cardboard is being used to make a container that will have no lid. Foursquare cutouts of side length h will be cut from the corners of the cardboard. The container will have a square base of side s, height h, and a volume of 80 in³. Which is the correct order of steps for finding minimum surface area A of the container? s²h = 80 and A = s² + 4sh 1. A' = 2s- II. 0=2s- III. A s² + O I, III, II O III, I, II s = 5.429 in and h = 2.714 in O III, II, I 320 s² O I, II, III 320 s² 320 S