1. Use Lagrange Multiplier to determine the dimensions of a rectangular box, open at the top, having a volume of 32 cubic feet and requiring the least amount of material for its construction.
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Expert's answer
2020-04-20T15:20:49-0400
Let dimensions of the box be a, b and c feet respectively.
Rectangular box, open at the op
Given : Volume=abc=32ft3
To find : least amount of material for its construction, which means minimum surface area.
Solution : S=ab+2bc+2ca is the surface area of the required box.
Thus, V(a,b,c)=abc−32=0
And S(a,b,c)=ab+2bc+2ca = minimum.
Using the Method of Lagrange's Multiplier, we get;
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