In this protect we want to discover the maximize possible volume of an open topp
ID: 2838645 • Letter: I
Question
In this protect we want to discover the maximize possible volume of an open topped. tabbed box folded from an 8.5 x 11 piece of paper. The construction goes as follows. Draw lines that are offset from each edge by length x. Then along one pair of sides draw another set of lines offset by 2x. Next fold up the two edges with a single offset line as pictured below (a) Find the formula for the volume of the box when you fold along the long edge (W = 11). Cal this (b) What is the domain of the function V1(x)? (c) Find the volume of the box when x =1 in when folding along the long we (W = 11 (d) Find the maximum possible value of V1(x) (e) Find the formula for the volume of the box when you fold along the short edge (W =8.5)Call this formula V2(x). (f) What is the domain of the function V2(x)? (g) Find the volume of the box when x=1 in when folding along the short edge (W=8.5). units. (h) Find the maximum possible value of V2(x) (i) Describe how to fold the box so that the volume is maximizedExplanation / Answer
a)
length = 11 - 2*x
Width = 8.5 - 4*x
height = x
v1(x) = (11 - 2*x)*(8.5 - 4*x)*x
b)
domain of the function is obtained by solving the inequation 11 - 2*x > 0.
x < 11/2
Domain = (0, 5.5)
(c)
Put x=1 in the equation v1(x) = (11 - 2*x)*(8.5 - 4*x)*x.
v1(1) = 40.5 cubic units.
(d)
Maximum possible value of the function v1(x) is obtained at x = 0.9403434291 and its value is 40.63507654 cubic units.
similar way you can solve the remaing answers with following measurements.
a)
width = 11 - 4*x
length = 8.5 - 2*x
height = 2*x
v2(x) = (11 - 4*x)*(8.5 - 2*x)*2*x
b)
domain of the function is obtained by solving the inequation 11 - 4*x > 0.
x < 11/4
Domain = (0, 2.75)
(c)
Put x=1 in the equation v2(x) = (11 - 4*x)*(8.5 - 2*x)*2*x
v2(1) = 91 cubic units.
(d)
Maximum possible value of the function v2(x) is obtained at x = 1.088901290 and its value is 91.48333608 cubic units.
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