A Firm Has an Order of 10,000 Units of Its

question 78

Essay

A firm has an order of 10,000 units of its product and has two plants at which to manufacture these units.Let
be the number of units to be produced at the first plant and
denote the number to be manufactured at the second plant.It is known that the cost function is given by
C = 48
+ 3
+ 25,000.Use the method of Lagrange multipliers to determine how many units should be produced at each plant to minimize this cost function.

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Definitions:

Embargo Act

Attempt in 1807 to exert economic pressure by prohibiting all exports from the United States, instead of waging war in reaction to continued British impressment of American sailors; smugglers easily circumvented the embargo, and it was repealed two years later.

Sedition Act

Refers to several historical laws in the United States that made it illegal to speak or act against the government, notably the 1918 act during World War I.

Republican Press

The segment of the media historically aligned with or supportive of the Republican Party and its policies in the United States.

Alexander Hamilton

A Founding Father of the United States, first Secretary of the Treasury, and key figure in the establishment of the national financial system.