A rectangular storage container without a lid is to have a volume of 10 m3. The length of its base is twice the width. Material for the base costs $15 per square meter. Material for the sides costs $9 per square meter. Find the cost (in dollars) of materials for the least expensive such container. (Round your answer to the nearest cent.)

The least expensive cost = $245.32

Step-by-step explanation:

From the information:

Volume of the rectangular container = 10 m²

Assume the width of the container is = w

The base = 2 × width

= 2(w)

Volume = height × base × width

10 = h × 2w × w

Now, to calculate the area of the base; we have:

Cost of base = --- (1)

Let's not forget that the cost of the sides = $9 per m²

Thus; the cost of the sides will be

the cost of the sides

Thus the total cost = cost of base = cost of sides

By differentiation;

From;