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MINIMIZATION PROBLEM (CALC)

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A wire 9 meters long is cut into two pieces. One piece is bent into a square for a frame for a stained glass ornament, while the other piece is bent into a circle for a TV antenna. To reduce storage space, where should the wire be cut to minimize the total area of both figures? Give the length of wire used for each:
For the square?
For the circle?

Where should the wire be cut to maximize the total area? Again, give the length of wire used for each:
For the square?
For the circle?

  • MINIMIZATION PROBLEM (CALC) - ,

    total area= PIr^2+ ((9-2r)/4)^2

    so find r when dA/dr=0

    lengths of two pieces: 2r, 9-2r

    you will get two solutions, one for min area, one for max area.

  • MINIMIZATION PROBLEM (CALC) - ,

    n-7w

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