(a) If the height and width of the aquarium are equal, find the dimensions that will minimize the cost to build an equation.

Volume of the aquarium cubic feet.

Formula for the volume of the rectangular prism is ,

where is length, is width and is height of the prism.

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The height and width of the aquarium are equal, then .

Find in terms of .

Substitute in .

.

The area of the base is . The area of two of the sides is while the area of the other sides is .

Use these expressions and the cost of glass to develop a cost function.

Substitute .

Find the minimum point by using graph.

Graph the equation and locate the minimum point.

Observe the graph:

The minimum point is at .

Height of the aquarium is ft.

Width of the aquarium is ft.

Substitute   in .

Length of the aquarium is ft.

(b) Find the minimum cost:

Minimum of the function is at .

The minimum cost is .

(c) If the aquarium is in cube shaped, then find difference in manufacturing costs:

Formula for volume of  the cube , where is the side of the cube.

.

The area of the base is . The area of two of the sides is while the area of the other sides is .

Substitute .

The difference is .

The difference between the manufacturing costs is

(a) Length of the aquarium is ft, height of the aquarium is ft and

width of the aquarium is ft.

(b) The minimum cost is .

(c) The difference between the manufacturing costs is