When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 39 b
atteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 6000 batteries, and 1% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
1 answer:
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Let x and y be the dimensions of the rectangle. If the perimeter is 40, we have
We can expression one variable in terms of the others as
Since the area is the product of the dimensions, we have
This is a parabola facing down, so it's vertex is the maximum:
So, the maximum is
And since we know that , we have
as well.
This is actually a well known theorem: out of all the rectangles with given perimeter, the one with the greatest area is the square.