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Safari File Edit View History Bookmarks Window Help mathxl.com ? ? EXAMINATION TNO-SPRING 2018 Course Home Do Homework Amr Hafez Mathway | Math Problem Solver Math 3415-01 Calculus III (Spring 2018) Homework: Section 12.8 Homework Score: 0 of 3 pts 12.8.35 Amr Hafez | 4/5/18 8:28 PM Save 5 of 7 (2 complete) Hw Score: 7.14%, 1 of 14 pts Question Help | * A delivery company requires that any box delivered must have a length plus girth (distance around) totaling no more than 132 inches. Find the dimensions of the box with maximum volume that can be sent The dimensions of the box with maximum volume that can be sent areinches. Simplify your answer. Use a comma to separate answers as needed.) Enter your answer in the answer box and then click Check Answer. All parts showing Clear All Check Answer

Explanation / Answer

Let length of box = x
Width = y
Ht = z

So, girth is 2y + 2z

And thus
we have
x + 2y + 2z = 132

We have to max volume

So, this is a true blue lagrange problem...

f(x,y,z) = xyz ---> to be max-ed
g(x,y,z) = x+ 2y + 2z

Finding partials :
fx = yz , fy = xz , fz = xy
gx = 1 , gy = 2 , gz = 2

Now, linkin' em like this fx = mgx , fy = m*gy etc
we get

yz = m(1)
xz = m(2)
xy = m(2)

Dividng first two :>
y/x = 1/2
x = 2y

Dividing last two :
z/y = 1
z = y

So, we have
x = 2y
y = y
z = y

So, using the constraint x+ 2y + 2z = 132, we get :
2y + 2y + 2y = 132
6y = 132
y = 132/6
y = 22

So, we have
x = 2*22 = 44

So, dimensions are :
44 , 22 , 22 ----> ANS

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