An Artist Produces Two Items for Sale $R ( x , y ) = 40 x + 7 x y + 80 y ^ { 2 } + 10 y$

question 15

Multiple Choice

An artist produces two items for sale. Each unit of item I costs $50 to produce, while each unit of item II costs $200. The revenue function is $R ( x , y ) = 40 x + 7 x y + 80 y ^ { 2 } + 10 y$ , where x is units of item I and y is units of item II. Suppose the artist has only $1000 to spend on production. Which of the following is the Lagrange function the artist should use to determine what combination of production amounts (x, y) will yield maximum profits subject to the constraint that his costs must equal $1000.

• A) -10x + 7xy + 80 \(y ^ { 2 }\) - 190y + λ(200x + 50y - 1000)
• B) 40x + 7xy + 80 \(y ^ { 2 }\) + 10y + λ(50x + 200y - 1000)
• C) -10x + 7xy + 80 \(y ^ { 2 }\) - 190y + λ(50x + 200y - 1000)
• D) 40x + 7xy + 80 \(y ^ { 2 }\) + 10y + λ(200x + 50y - 1000)
• E) none of these

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Definitions:

Socialization Process

The process by which individuals learn and internalize the values, beliefs, and norms of their society or social group, helping them to function as members of that society.

Prison Values

The core principles and standards that guide the operations, policies, and culture within a prison system.

Ostracism

A form of social exclusion in which a person is temporarily banished or excluded from a community or group through a formal or informal process.

Felony Incarceration

The confinement in prison of individuals who have been convicted of a felony, which is a crime typically more serious than a misdemeanor.