Question

The design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 4.5 inches. If the length must be 1.5 times the height, what should each dimension be?
Hint: Let x represent one of the dimensions, then define the other dimensions in terms of x.

Answer 1

We are going to define the following variables:
 x = height
 1.5x = length
 4.5 - 2.5x = width
 Then, the volume will be:
 V = (x) * (1.5x) * (4.5-2.5x)
 Rewriting we have:
 V = x * (6.75x - 3.75x ^ 2)
 V = -3.75x ^ 3 + 6.75x ^ 2
 Answer:
 The dimensions are:
 (x) * (1.5x) * (4.5-2.5x)
 Where,
 x = height
 1.5x = length
 4.5 - 2.5x = width