A^2 + b^2 + c^2 - ab - bc - ca = 0
a.a + b.b + c.c = a.b + b.c + c.a
equating term by term:-
a = b
b = c
c = a
Therefore a = b = c
we know that
the volume of a rectangular prism is equal to

where
L is the length of the box
W is the width of the box
H is is the height of the box
in this problem we have




<u>Find the length of the box</u>
Using a graph tool-------> we will determine the roots of the equation of volume
see the attached figure
the roots are

so

therefore
<u>the answer is</u>
the length of the box is equal to 
1. 2.00/64=3.125 cents per oz
2. 7.50/256=2.930 cents per oz.
3. The best deal is at the whole sale
S = 10 + r
s + r = 100
Adding equations,
2s +r = 110 + r
2s = 110
s = 55
r = 45