The application of the functions of two variables for solving economical problems

Problem 12.1. The company manufactures the products of two types A and B. The general daily costs (in UAH) of the company for production units of the product A and units of the product B is known

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Find a number unit of the products A and B, which they need to product, that total costs of the company will be minimum.

Solution: Fist of all let us find partial derivatives of the first and second order

;

;

;

;

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Find critical points of the fist order, by solving a system of the equations

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A stationary point

Compose and evaluate determinant which elements are partial derivatives at a point.

=

The function has extreme and, what’s more, it is minimum, because .

Find

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The company will has minimum costs 1398 UAH if they will product 23 units of product A and 21 units of product B.

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