Arectangular storage container with an open top is to have a volume of 10 m3 . then length of its base is twice the width. material for the base costs $10 per square meter. material for the sides cost $6 per square meter. find the cost of materials for the cheapest such container.

The cost of materials for the cheapest such container is $163.54.

Step-by-step explanation:

A rectangular storage container with an open top is to have a volume of 10 m³.

The volume of the rectangle is

Length of its base is twice the width.

Let Width be 'w'.

Length is l=2w.

Height be 'h'.

The height in terms of width is represented as,

According to question,

The cost is 10 times the area of the base and 6 times the total area of the sides.

i.e. Cost is given by,

To get the minimum value,

Differentiate the cost w.r.t 'w',

To find critical points put derivate =0,

We find the second derivative to minimize,

As it is the minimum cost.

The cost is minimum at w=1.65.

Substitute the values in the cost function,

Therefore, the cost of materials for the cheapest such container is $163.54.

explanation:

remove parenthesis:

=

apply rule

=

multiply fractions:

=

=

divide:

=

mordancy.

the first domain and range set to the left is matched with the top relation, and the second set the set in the middle goes with the bottom relation.