Formulate and solve a problem of choice of the optimal supply and of the optimal price set by a monopolistic company considered in Example 5.3. Assume a nonlinear function of production total cost of a form:  Analyse sensitivity of the optimal supply and of a product optimal price to changes in values of parameters describing the market: a market capacity, strength of consumers' reaction to changes in a product price, production marginal cost.

Example 5.3
The following functions are given:

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ctot (y) = y2 + , , > 0.