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Chrome File Edit View History Bookmarks People Window Help +94) 8796 ,t Wed Jun 10 23:24:25 a E 2.6 Welcome to Finish Line plete | Jimmy John M Test Resource -trej301g C Chegg.com www.webassign.net/web/Student/Assignment-Responses/submit?dep=1 1 522585 Home Download FreeT_MY UM t Download Free NMY UM KE TerpMail EE Welcome to Terra C-The DK HandbookHomeNG ELMS WA WebAssign-LOG IN 3. 3. 1.5/1.5 points | Previous Answers +1.5/1.5 points | Previous Answers My Notes Times New Ro B IU The shipping company BigBlue has a size requirement for rectangular packages: the sum of the three dimensions cannot exceed 120 inches. If one end of the package is a square with sides of x inches, and the other dimension is y inches, what are the dimensions that will maximize the volume? x=40 in. and y = 40 in The maximal volume is 64000 in Al . -11.5 points A crate open at the top has vertical sides, a square bottom, and a volume of 864 cubic meters. If the crate has the least possible surface area, find its dimensions Hint: Each surface of the box is what shape? My Notes meters meters meters 5, + 1.7 points My Notes Shakespeare is buiding a shed with a square base measuring x feet by x feet, and which is h feet high. He wants the volume of the shed to be 192 ft3. Concrete for the base costs $3 per ft2. The materials for each of the four sides cost $2 per ft2. The flat roof will cost $9 per ft2 DS If Shakespeare wants to minimize cost, the the objective function in terms of x and h is: The constraint equation in terms of x and h is: 192 = The dimensions which minimize cost are x = ft and h = ft.

Explanation / Answer

1)

Length = x meters
Width = y meters
Height = z meters

xyz = 864
the bottom is square. Therefore
y = x------------------------------------- (1...
Or x*x*z = 864
Or x^2 * z = 864
Or z = 864/x^2----------------------- (2)

There is one surface with dimensions x,y (because other one is open).
Two surfaces with dimensions y,z.
Two surfaces with dimensions x,z.

Therefore surface area S = xy + 2yz + 2zx
Using (1) and (2) in the above,
S(x) = x*x + 2*x*864/x2 + 2*864/x2 * x
= x2 + 1728/x + 1728/x
Or S(x) = x2 + 3456/x
Differentiating
# S'(x) = 2x - 3456/x2
For least S(x):-
S'(x) = 0
Or 2x - 3456/x2 = 0
Dividing by 2,
x - 1728/x2 = 0
Or x = 1728/x2
Or x3= 1728
Or x = 12
From (1), y = x = 12
From (3), z = 864/144 = 6

Ans: 12 meters, 12 meters, 6 meters

2)

The cost function is

C = 3x

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