Please help me please help
2 answers:
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Answer:
The cost is minimized for
and then
and the ratio height / radius = 2.3
Step-by-step explanation:
When you solve these kind of problems you always need to ask yourself what am I minimizing or maximizing, for this case you need to minimize the cost function.
Suppose that the bottom of your drum has a radius and a height and a height
then the are of the circle at the bottom would be
And the area of the sides would be given by
According to what they say the cost of the sides is 2$ per square meter and the cost of the bottom is 3$ per square meter.
So the cost would be given by this function.
Cost =
But they mention that the volume = 2 cubic meters. On the other hand
Volume = = 2 if we replace on Cost we get that
When you find the derivative of that and equal to zero you will find that the the cost is minimized for
and then
and the ratio height / radius = 2.3