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Evaluating a Utility Function Model
An economist is modeling the preferences of a consumer who enjoys both coffee (C) and pastries (P). The consumer states that, regardless of how much they already have, their total satisfaction always increases when they get more coffee, and it also always increases when they get more pastries. The economist proposes the following function to represent the consumer's satisfaction: U(C, P) = 10C + 8P - 0.5P². Evaluate whether this function is a suitable model for this consumer's preferences for all possible non-negative quantities of pastries. Justify your answer by analyzing the rate at which satisfaction changes as the quantity of pastries increases.
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