Example 0.6.1. A company produces x units of commodity A and y units of commodity B. All the units can be sold for p = 100 - x dollars per unit of A and q = 100 – y dollars per unit of B. The cost (in dollars) of producing these units is given by the joint-cost function C(x, y) = x² + xy + y². What should r and y be to such that the profit π = xp+yq - C(x, y) attains a local maximum?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Example 0.6.1. A company produces x units of commodity A and y units of commodity B. All the
units can be sold for p = 100- x dollars per unit of A and q = 100 - y dollars per unit of B. The cost
(in dollars) of producing these units is given by the joint-cost function C(x, y) = x² + xy + y². What
should x and y be to such that the profit = xp+yq-C(x, y) attains a local maximum?
Transcribed Image Text:Example 0.6.1. A company produces x units of commodity A and y units of commodity B. All the units can be sold for p = 100- x dollars per unit of A and q = 100 - y dollars per unit of B. The cost (in dollars) of producing these units is given by the joint-cost function C(x, y) = x² + xy + y². What should x and y be to such that the profit = xp+yq-C(x, y) attains a local maximum?
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