Question 1010811: If a company makes a block of cheese designed to have the height exactly five times the width and the ideal of 1800mm^3 using the least possible surface area, what would be the length
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website! Most of the way through, but short of complete finish:
y, height
x, length
z, width
The description gives from these chosen variables,
and the area function you want, depending on name you choose,
 .
Substitutions to put A as a function of just one single variable...
but z is width, and the question asks for LENGTH to minimize area.
Try again...
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Use in the volume,
still giving a square for what we want to substitute.
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Try first aiming for one of the other variables for the single variable in A.
Go back to description, and substitute for y in A.
 -------want to eliminate, subst for x or z...
Look again at description.
 ------Substitute for x in A.
 -------Variable z must be used, take derivative, and find what makes A the minimum, and then find the corresponding x value, the asked for length.
---------
continuing,
 You fill in the steps to that.
Set deriv to 0.
The denominator does not take meaning here ...
and you can fill-in the steps...
Again use the equations from the description to reach the corresponding value for x, the length.
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