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Suppose the Partial Derivatives of a Lagrange Function F(x, Y Fx\frac { \partial F } { \partial x }

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Suppose the partial derivatives of a Lagrange function F(x, y, λ) are Fx\frac { \partial F } { \partial x } = 2 - 8λx, Fy\frac { \partial \mathrm { F } } { \partial \mathrm { y } } = 1 -2λy, Fλ=324x2y2\frac { \partial F } { \partial \lambda } = 32 - 4 x ^ { 2 } - y ^ { 2 } What values of x and y minimize F(x, y, λ) ? (Assume x and y are positive.)

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Definitions:

Forecasted Net Income

An estimated calculation of a company's earnings after all expenses and taxes have been subtracted from revenue for a given future period.

Total Dividends

The sum of all dividend payments made to shareholders for a particular period, typically a fiscal year.

Retained Earnings

Earnings accumulated by a company thus far, minus any shareholder dividends or distributions already issued.

Share Price

The current price at which a single share of a company can be bought or sold in the market.

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