At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions.

See more answers at brainly.com

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions

ok ill help you :)

this is an optimization problem, did you see that in class?

Yes I do recognize that its an optimization problem, in which we have to alter our formulas.

Help?

do you need an answer?

or set up

setting up and understanding, please.

okay, so first lets take care of the constraint. i.e. the volume of this box is 50 cm^3

yes

how about \[V=3x^2y\] and we know that \[50=3x^2y\]

is that good?

where did the 3x^2 come from?

woah sorry i had to go fix a computer ill let ebbflo take over hes got a good flow going,

** I meant 3x^2y

the length is 3 time the width

so 3x^2 is the area of the base and I just let y be the heigth of the box

is that good?

yes

Area = base * height
so the base =3x and the height=x

i am just adding up the areas of the sides of the box

the base of the box has dimensions (3x)cm by (x)cm

are you good with the surface area formula I presented?

If so We can proceed to the cost function

im sorry meters

can you explain to me how you arrived to your Surface area

so that's where I got my formula for the surface area

allright.

sorry I made a slight mistake in that formula

the last one I wrote was correct

now we are ready to write the cost function above as a function of x only by way of the constraint

okay.

so since \[50=3x^2y\]\[y=\frac{50}{3x^2}\]

so \[C(x)=30x^2+48x(\frac{50}{3x^2})\]
and cleaning it up we get \[C(x)=30x^2+\frac{800}{x}\]

if we are good, then now it is time to derive

since this is a box with known volume we know \[x\neq 0\] so just solve \[60x^3-800=0\] for x

we get \[x=2(\frac{5}{3})^\frac{1}{3}\]

use that vale to get the other dimensions and you are done...

thank you soo much

glad it helps, this is easier to explain with the aid of a sketch