Let F(x, Y, Z) = Xyz

question 56

Short Answer

Let f(x, y, z) = xyz. Find the point(s) where f(x, y, z) may have a possible relative maximum or minimum, subject to the constraint x + 6y + 3z = 36 and where x > 0, y > 0, z > 0. Use the method of Lagrange multipliers.
Enter your answer as just (a, b, c) where a, b, c are all integers.

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Definitions:

Wampum

Traditional shell beads of the Eastern Woodlands tribes of Native Americans, used for trading, storytelling, and ceremonial purposes.

Pilgrims

Early settlers of the Plymouth Colony in present-day Massachusetts who arrived on the Mayflower in 1620, seeking religious freedom.

Puritans

A religious reform movement in the late 16th and 17th centuries, seeking to "purify" the Church of England of Roman Catholic practices, many of whose adherents later settled in North America.

Church Of England

The primary state church in England, a Christian church characterized by a distinctive Anglican faith and identity, with the monarch serving as its supreme governor.