Hello, Lafexlos!

Let = length, = width, = height.A closed box to be found to have length 2ft, width 4ft and height 3ft.

The measurement of each dimension has a maximum possible error of ±0.02ft.

The top of the box is made from material that costs $2/ft².

The material for the sides and bottom costs $1.50/ft².

What is the maximum error involved in the computation of the cost of the box?

We are given: .

The area of the top is ft².

. . Its cost is: . dollars.

The rest of the box has a total area of: ft².

. . Its cost is: . dollars.

The total cost is: .

. . We have: .

Take differentials: .

Substitute the given data:

. .

Therefore, the maximum error of the cost is: .