How do you solve this optimization problem?
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use calculus to find the dimesions of a rectangle with perimeter of 10 and maximal area.
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Answer:
A rectangle's perimeter is 2l+2w 2l+2w=10 You want to maximize area A rectangle's area is l*w a=l*w Solve 2l+2w=10 for one of the variables 2l+2w=10 10-2l=2w w=(10-2l)/2 so.. a=l*(10-2l)/2 a=(10l-2l^2)/2 Take the derivative of this, find the critical points, and you'll get an answer and be able to solve the rest working backwards through the equations you used.
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