A microwaveable cup-of-soup package needs to be constructed in
the shape of cylinder to hold 250 cubic centimeters of soup. The
sides and bottom of the container will be made of styrofoam costing
0.03 cents per square centimeter. The top will be made of glued
paper, costing 0.07 cents per square centimeter. Find the
dimensions for the package that will minimize production
cost.
Helpful information:
h : height of cylinder, r : radius of
cylinder
Volume of a cylinder: V=πr2hV=πr2h
Area of the sides: A=2πrhA=2πrh
Area of the top/bottom: A=πr2A=πr2
To minimize the cost of the package:
radius:
height:
minimum cost:
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