(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant 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]

3. 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?

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# Maximizing volume

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