This is a simple example of a posynomial function, involving the construction and operating costs of a cylindrical liquid (say, oil, or water) storage tank.
The parameters of the tank are its diameter and height . The costs to manufacture, and then operate during a given period of time (say, a year) the tank, include the following.
where is some positive constant, expressed in (say) dollars, and .
Construction costs include the costs associated with building a base for the tank, and costs associated with building the tank itself. In our model, the first type of costs depends only the base area , while the second depends on the surface of the tank, . (This assumes that we can use the same base height for a variety of tank heights.) Thus the construction cost function can be written
where the constants , , with constants expressed in dollars per square meters.
The total manufacturing and operating cost function is thus the posynomial function
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Level sets of the cost function of the problem, corresponding to the values
The function clearly appears not to be convex, since some level sets are not.
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See also: Optimization of a water tank.
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