Answer:
Length = 12
Width = 8
Height = 4
Step-by-step explanation:
Let length of box = l
Width = 2/3 * l
Height = 1/3 * l
Volume of the box = 384 ft³
Volume = Length * width * height
Volume of box = l * 2/3 l * 1/3 l
384 = 2l³ / 9
384 * 9 = 2l³
3456 = 2l³
l³ = 3456 / 2
l³ = 1728
Take the Cube root of 1728
l = 12
Length = 12
Width = 2/3 * 12 = 8
Height = 1/3 * 12 = 4
Answer:
Step-by-step explanation:
The constraints are
The red line represents the function
At 
At 
Two points are 
The blue line represents the function
at
at
Two points are 
The other two constraints are 
, 
. So, the point has to be in the first quadrant
From the graph it can be seen there are two points where the function will be maximum let us check them.
So, the maximum value of the function is .
<span>So, the volume of a container can also be thought of as the amount of liquid that the container is capable of holding. It follows that 450=(length)(width)(height). The constraints of the problem say that the length of the box must be twice as large as the width, so it follows that j(height)=(2w)(w)(height)-450. This then implies that j(height)=(2w^2)(height)-450. In simpler terms, the height is defined as 450/(2w^2), or j(w)=450/(2w^2).</span>
Answer: 3
Step-by-step explanation:
