Arectangular storage container with an open top has a volume of 14 m3. the length of its base is twice its width. material for the base costs $5 per square meter; material for the sides costs $4 per square meter. express the cost of materials as a function of the width of the base.

Explanation:

First at all, let's see the figure in the attachment where we define:

Width is "x", Lenght must be "2x" and Height is "h".

The volume of a rectangular storage container is defined as:  

V=lengh*width*height

So, replacing values, we have:

V=

Considering that V=14m3 we can clear "h" in function of "x" (the width):

Now, we calculate the areas of the container:

Where: Ax1 is the side 1 area; Ax2 is the side 2 area and Ax3 is the base area

Replacing "h" on the previous equations, we have:

Remember that the container is open at the top, so we have to calculate just one area in the base. The sides 1 and 2 are 2 of each one.

So, we have: Total area = 2*Ax1 + 2*Ax2 + Ax3

Now for the total cost of materials, we have: Total cost=Cost (2*Ax1) + Cost (2*Ax2) + Cost (Ax3)

For the sides 1 and 2, we have a cost of:

Finally, total cost is: