What is the area of the rectangular base in terms of the width?
a rectangular storage container with an open top is to have a volume of 10 cubic meters. the length of its base is twice the width. material for the base costs $10 per square meter. material for the sides costs $6 per square meter. find the cost of materials for the cheapest such container.
how do you find the length, width and height for volume?
Yes, there will be the base, whose area you have already found is and the 4 sides. Now, you should have the area of the sides is:
Both of these are in square meters. So, now you want to construct the cost function. Take the cost of the material per square meter times the area in square meters to get the cost, then sum these together to get the total cost in dollars:
Now, minimize this function.
You should have:
and so:
Since we want , we take the critical value from the numerator:
Using the first derivative test, we find this critical number is at a minimum. Hence:
Now evaluate the cost function at this critical value to find the minimum cost in dollars.
Please show how you arrived at 3.5569 as your critical number, so we can address the error in the method/computation.