Determine the Maximum Value of F(x, Y) = 4 - $x ^ { 2 }$

question 41

Short Answer

Determine the maximum value of f(x, y) = 4 - $x ^ { 2 }$ - $y ^ { 2 }$ subject to the constraint $y = 3 x - 4$ .
Enter your answer as exactly just a, b where a is the maximum and b is the Lagrange multiplier as either integers or reduced fractions of form $\frac { \mathrm { c } } { \mathrm { d } }$ (no words or labels).

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Definitions:

Pro Forma Income Statement

A financial statement that projects the future income and expenses of a company, often used for forecasting or budgeting purposes.

Common-Size Statement

A standardized financial statement presenting all items in percentage terms. Statement of financial position is shown as a percentage of assets and income statement as a percentage of sales.

Sustainable Growth Rate

The maximum rate at which a company can grow its earnings, dividends, and sales without having to increase its equity or take on new debt.

External Financing

Funds raised from sources outside of the company, such as loans, investors, or grants, to support business activities.