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dimpledur
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Homework Statement
Canada Post accepts international parcels whose (Length+Girth) is less than or equal to 2 meters, and Length is less than or equal to 1 meter. Girth is defined as the cross section. We wish to ship a parcel of the shape of a triangular prism of length l meters. The cross section is a right triangle with catheti of lengths a and b meters. Assume the package walls are thin. What is the maximal volume of a parcel?
Homework Equations
Let
[tex]leg_1=a=y, leg_2=b=z, length=x[/tex]
I provided a drawing via paint for you to envision my take on the problem
Hence,
[tex]V(x, y, z)=\frac{1}{2}xyz[/tex]
Boundaries:
[tex](x+y+z+\sqrt{x^2+y^2})\leq{2}, x\leq{1}[/tex]
The Attempt at a Solution
[tex]\nabla{f}(x, y, z)=\frac{1}{2}(yzi+xzj+xyk)[/tex]
and hence there exists a critical point at (0, 0, 0).
Next, I get partially lost. Should I be finding second partial derivatives of the boundary and then evaluating the Hessian matrix to determine extremes on the boundary?