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bagirrra123 [75]
3 years ago
12

Economite plastics plans to produce a one-compartment vertical file by bending the long side of an 8-in. by 14-in. sheet of plas

tic along two lines to form a u shape. how tall should the file be in order to maximize the volume that the file can hold?

Mathematics
1 answer:
poizon [28]3 years ago
3 0

Volume of the file = Volume of the rectangle = length *width * height

=l*w*h

V=(14-2x)*8*x\\ =112x-16x^2

So the Volume of the file V=112x-16x^2

Now to maximize the file: Compute dV/dx and set to 0.

\frac{dV}{dx}=112-32x\\

Set dV/dx=0 implies 112-32x=0 \Rightarrow 32x=112\Rightarrow x=3.5

Thus x=3.5 in tall should the file be in order to maximize the volume that the file can hold.

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