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okay we have this optimization question which reads we have a piece of cardboard that is 14 inches by 10 inches and we are going to cut out the corners and fold up the sides to form a box determine the height of the box and calculate the boxamp;#39;s maximum volume so whatamp;#39;s happening is if we got a sheet of paper as such on screen and weamp;#39;re going to take out a little bit from each corner and then weamp;#39;re going to fold it up so it forms a box okay so the question is asking determine the height of the box which is where the optimization occurs and calculate the maximum volume so itamp;#39;s asking for two things and we are going to start off by drawing a diagram like this so itamp;#39;s 14 inches across 10 wide and we are being asked to calculate its height and by the height what we are being asked is to find the value of this length here because that is being cut out which will form the height and weamp;#39;ll just say um for this question that our val
