11) Application problem: I came across this interesting exercise from a fellow math professor and modified it to suit our course assignment. This is a variation of the classic cardboard box problem you worked on MXL homework. (10 pts) You are asked to design a box from cardboard sheet of size: 15 inches wide by 25 inches long, by cutting and folding them as shown in the picture below. The dark rectangles are the parts of the cardboard you'd cut away, and the light parts are the parts you'd keep. You would fold these along the dotted lines to make four sides, a bottom, a top, and flap to fold over and glue the top to the front of the box. The front flap (that is to be glued) needs to be 1 inch wide. Well, the box you design can look wider on the ground or shallow and tall but it needs to hold maximum quantity inside it. So, what's the best way to slice up your cardboard (leaving that flap in the design)? 2 3 Hint : 1 inch X X X- Use calculus 15 in to find Max Vol. bottom * flap based on given X X information. X 1 inch Show all steps, graphs & write statements to explain your answer ( with correct (The original source for this problem will be released after the test due date on Bb.) units