The Following Results Are Obtained When Optimizing F(x, Y)subject to the Constraint

question 33

Essay

The following results are obtained when optimizing f(x, y)subject to the constraint g(x, y)= 35.The maximum value is f(5, 7)= 39, the Lagrange multiplier $\lambda$ = 4 (when $\nabla f = \lambda \nabla g$ )and $\nabla f = 2 \vec { i } - 5 \vec { j }$ .What is g(5, 7)?

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Definitions:

Unit Costs

The cost incurred by a company to produce, store, and sell one unit of a particular product or service.

Price Ratio

The relative price of one good or service compared to another, often used in economic analysis.

Cost Function

An equation that calculates the total cost of producing goods or services as a function of the quantity of output produced.

Production Function

A mathematical relation that expresses the relationship between inputs used in production and the output produced.