Question

A company wishes to manufacture a box with a volume of 36 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material. Use your work from the previous question.

Answer 1

Answer:

Width is 3 ft

length is 6 ft

Step-by-step explanation:

Let x = the width

Let 2x = the length

Let h = the height

We know that volume is given v =  l×b×h

so we have v = volume  $= x*2x*h$

$2x^2*h = 36$

$h = \frac{18}{x^2}$

surface area include 2 ends + 1 bottom and 2 sides excluding top

$S.A. = 2(x*h) + 1(2x*x) + 2(2x*h)$

$S.A. = 2xh + 2x^2 + 4xh$

we have calculate$h = = \frac{18}{x^2}$

$S.A = 2x^2 + 6x \frac{18}{x^2}$

$S.A = 2x^2 + \frac{108}{x}$

By graphing above equation we can calculate the value of x

Minimum S.A when x is 3  is the width so

2(3) = 6 is the length

$h = \frac{18}{3^2} = 2$