Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.6 Maxima, Minima, and Saddle Points, #58 · Multivariable Calculus · Gradient & optimization

The desirability of … houses and … yachts is

The desirability of $x$ houses and $y$ yachts is $f (x, y)$ . The constraint $p x + q y = k$ limits the money available. The cost of a house is ____, the cost of a yacht is ____. Substitute $y = (k - p x) / q$ into $f (x, y) = F (x)$ and use the chain rule for $d F / d x$ . Show that the slope $- f_{x} / f_{y}$ at the best $x$ is $- p / q$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.6 Maxima, Minima, and Saddle Points, #58

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