SOLUTION: HI,
A wire of length 40 inches is to be cut into two pieces, each of which will be used to form a circle. Suppose we will be charged $2 for each square inch of area enclosed by th
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Question 864949: HI,
A wire of length 40 inches is to be cut into two pieces, each of which will be used to form a circle. Suppose we will be charged $2 for each square inch of area enclosed by the first circle, and $1 for each inch in the second circle's circumference. Find the lengths of the two pieces of wire which will
minimize the total cost.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A wire of length 40 inches is to be cut into two pieces, each of which will be used to form a circle. Suppose we will be charged $2 for each square inch of area enclosed by the first circle, and $1 for each inch in the second circle's circumference. Find the lengths of the two pieces of wire which will
minimize the total cost.
--------------
C = length of wire in the 1st circle ($2 per sq inch)
-->
-----
--> $1/inch of 40 - C for the 2nd circle
----
Price =
P(C) =
P'(C) =
C = pi inches for the 1st circle
40 - pi inches for the 2nd
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