Question

the design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 6 inches. if the length must be 1.5 times the height, what should each dimension be?

Answer 1

A+B+C = 6
A*B*C = some number to be maximized
A*B = 1.5

From the first equation:
Therefore, A+1.5/A +C = 6
C = 6-A-1.5/A

From the second equation:
A * (1.5/A) * (6-A-1.5/A) = Maximum volume
Use derivatives to obtain maxima.