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A corporation manufactures candles at two locations. The cost of producing x₁ units at location 1 is C₁ = 0.02x₁ 2 + + 4x₁ + 500 and the cost of producing X, units at location 2 is C₂ = 0.05x2² + 4x2 + 225. The candles sell for $12 per unit. Therefore, the profit is given by the following. P = 12(x₁ + x2)-C₁ - C₂₂ State the profit equation in terms of only x, and x2. (Your answer should not contain C, or C₂.) P(x1, x2) = Find the first partial derivatives of P. P+ PX2 Find the quantity that should be produced at each location to maximize the profit. X1 X2

A corporation manufactures candles at two locations. The cost of producing x₁ units at location 1 is C₁ = 0.02x₁ 2 + + 4x₁ + 500 and the cost of producing X, units at location 2 is C₂ = 0.05x2² + 4x2 + 225. The candles sell for $12 per unit. Therefore, the profit is given by the following. P = 12(x₁ + x2)-C₁ - C₂₂ State the profit equation in terms of only x, and x2. (Your answer should not contain C, or C₂.) P(x1, x2) = Find the first partial derivatives of P. P+ PX2 Find the quantity that should be produced at each location to maximize the profit. X1 X2

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
ChapterP: Prerequisites
SectionP.9: Modeling With Equations
Problem 5E
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A corporation manufactures candles at two locations. The cost of producing x₁ units at location 1 is C₁ = 0.02x₁ 2 + + 4x₁ + 500 and the cost of producing X, units at location 2 is C₂ = 0.05x2² + 4x2 + 225. The candles sell for $12 per unit. Therefore, the profit is given by the following. P = 12(x₁ + x2)-C₁ - C₂₂ State the profit equation in terms of only x, and x2. (Your answer should not contain C, or C₂.) P(x1, x2) = Find the first partial derivatives of P. P+ PX2 Find the quantity that should be produced at each location to maximize the profit. X1 X2
Transcribed Image Text:A corporation manufactures candles at two locations. The cost of producing x₁ units at location 1 is C₁ = 0.02x₁ 2 + + 4x₁ + 500 and the cost of producing X, units at location 2 is C₂ = 0.05x2² + 4x2 + 225. The candles sell for $12 per unit. Therefore, the profit is given by the following. P = 12(x₁ + x2)-C₁ - C₂₂ State the profit equation in terms of only x, and x2. (Your answer should not contain C, or C₂.) P(x1, x2) = Find the first partial derivatives of P. P+ PX2 Find the quantity that should be produced at each location to maximize the profit. X1 X2
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