Maximizing Volume of a Cube with constraints?

Question

You want to construct a Cube, this includes a top and a bottom. The material for the base costs $2 per sqft. The material for the top and four sides costs $1 sqft. You have $144 to spend, maximize the volume of the cube.

Answer 1

Okay, a cube has 6 faces. Since you're paying double for the base, call it 7. $144/7 = 20.57 dollars per face, so each face is going to be 20.57sqft. So an edge of your cube is 4.5354 ft long (take sqrt). Then cube that to get the volume = 93.3cuft

Answer 2

Base would be 20 sq ft i.e. (10 ft by 10ft) 20 x $2 = 40

The other 5 sides must be of the same size i.e. 20 sq ft, therefore you have 5 sides @ 20 x $1 = $100

$100 + $40 = 140 - you cannot make the cube any bigger with the money you have been supplied with, unless you can start cutting tiles into bits - but surely if you have to buy the tiles you would have to buy them as 'whole units'.

So I'm saying a maximum at a 20 cubic foot cube for $140 - and $4 for a hard earned beer later ;o)

Answer 3

I think you meant a cuboid with a square base.

In that case, the maximum possible volume of this cuboid will be approximately 148.723 cu.ft.

The base area of this cuboid will be 48 sq.ft, costing $ 96, while the top and four sides have an area of 9.6 sq.ft, costing the remainding $ 48.

Answer 4

let 'a' be the side length
now 5a^2*1 +a^2*2<=144
or, 7a^2<=144
for maximum volume a has to be maximum
so,a^2=144/7
or, a=4.5356
and max volume=93.03 cu. ft.

Answer 5

2x^2 + 5x^2 = 144
7x^2 = 144
x = 12/√7 = 4.5356 ft

Answer 6

you can use of a Linear Programming (LP). I can model and solve this simple problem but it better than you do it.