Question

Optimisation , No clue to solve this

Answer 1

A sheet of area 40m^2 is used to make an open tank with a square base , the find the dimensions of the base such that the volume of the tank is maximum

Answer 2

@ganeshie8 @Kainui

Answer 3

Draw a picture and label it as best as you can. =)

Answer 4

okay wait

Answer 5

Hey i am completely blank on this one , i don't know

Answer 6

draw a tank with open top

Answer 7

and with a square base

Answer 8

so basically a cube with one face missing

Answer 9

Net of a cube ?

Answer 10

don't know if all sides are square

Answer 11

a cube has all faces as square

Answer 12

that's what don't know if the tank has all squares , so how can i draw a cube

Answer 13

ok, not a cube,
square base, say side 'x' anf height 'y'

Answer 14

you will get one equation in x and y from the fact that surface area, with one face (the other base) missing is 40m^2

Answer 15

x^2 + xy +xy +xy +xy = 40

Answer 16

and volume will be ?

Answer 17

you can easily isolate y from
x^2 + xy +xy +xy +xy = 40

Answer 18

no, volume will be x^2 y ,right ?

Answer 19

yes

Answer 20

Sorry I wasn't paying attention and I think hartnn already said what I did, but I'll post it anyways and go eat lunch, good luck!

\[\Large V=x^2h\]\[\Large 40=A = 4xh+x^2\]

Answer 21

2x^2+4xh = 40 right?

Answer 22

since the top is OPEN, the other base will not be considered in surface area

Answer 23

oh yes open tank haa

Answer 24

40 = 4xh + x^2

Answer 25

yep, isolate y from that

Answer 26

i mean h

Answer 27

ya

Answer 28

(40-x^2)/4x =h

Answer 29

correct
now plug that in Volume formula

Answer 30

and the find the maxima , i will do that all
1 min

Answer 31

\[V=\frac{ 40x-x ^{3} }{ 4 }\]

Answer 32

yep

Answer 33

maxima occurs at