In Exercises 40 through 49, assume that the required extreme value is a relative extremum.

The social desirability of an enterprise often involves making a choice between the commercial advantage of the enterprise and the social or ecological loss that may result. For instance, the lumber industry provides paper products to society and income to many workers and entrepreneurs, but the gain may be offset by the destruction of habitable territory for spotted owls and other endangered species. Suppose the social desirability of a particular enterprise is measured by the function

where x measures commercial advantage (profit and jobs) and y measures ecological disadvantage (species displacement, as a percentage) with x ≥ 0 and y ≥ 0. The enterprise is deemed desirable if D ≥ 0 and undesirable if D

What values of x and y will maximize social desirability? Interpret your result. Is it possible for this enterprise to be desirable?

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D(x, y) = (16 — 6x)x − (y² − 4xy + 40) - -