Answer:
Step-by-step explanation:
Let the rectangle have (x,y,z) as vertex in positive octant. The rectangular box has to be necessarily symmetrical about all the three axes.
Then the sides of the box would be
Volume = 
Maximize volume subject to
i.e. 
Use Lagrangian multipliers , we have
at the maximum
Dividing we get
Similarly 
Thus we get 
Hence dimensions are
(2x,2y,2z)
So dimensions are
1. We assume, that the number 432 is 100% - because it's the output value of the task.
<span>2. We assume, that x is the value we are looking for. </span>
<span>3. If 432 is 100%, so we can write it down as 432=100%. </span>
<span>4. We know, that x is 45% of the output value, so we can write it down as x=45%. </span>
5. Now we have two simple equations:
1) 432=100%
2) x=45%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
432/x=100%/45%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 45% of 432
432/x=100/45
<span>(432/x)*x=(100/45)*x - </span>we multiply both sides of the equation by x
<span>432=2.22222222222*x - </span>we divide both sides of the equation by (2.22222222222) to get x
<span>432/2.22222222222=x </span>
<span>194.4=x </span>
x=194.4
<span>now we have: </span>
<span>45% of 432=194.4</span>
Cost of 2 1/2 yards= $15
cost of 1 yard=?
cost of one yard= 15/(2 1/2)
=15/5/2
=15/5*2
=3*2
=$ 6
so the cost of fabric for one yard will be $6
what that other person saicd
