Answer:
11,664 in³
Step-by-step explanation:
For a square side length of x, the girth is 4x and the length of the parcel is then allowed to be up to 108-4x.
The total volume is the product of the edge lengths, so is ...
V = (108 -4x)(x²) = -4x³ +108x²
This will be a maximum where its derivative is zero:
dV/dx = -12x² +216x = 0 = -12x(x -18)
This is zero for x=0 and for x=18.
The maximum volume parcel is 18 in by 18 in by 36 in, and has a volume of ...
(18 in)(18 in)(36 in) = 11,664 in³
Answer:
Dimensions are 20 X 44 feet
Step-by-step explanation:
First we need to build two equations:
For area X times Y = 880
For Perimeter 2x + 2y = 128
Now we need to solve one so we can substitute it into the other:
2x + 2y = 128 becomes
2x = 128 - 2y and then
x = 64 - y We will substitute this into the are equation
(64 - y)y = 880
64y - = 880
-
factor out the negative
-(
Factor:
-(y - 20)(y - 44) = 0
y-20 = 0 and y - 44 = 0
y = 20 and y = 44
Plugging these in two both of our formulas works
20 X 44 = 880 for area
2(20) + 2 (44) = 128 for perimeter