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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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter8: Polynomials
Section8.1: Adding And Subtracting Polynomials
Problem 19CYU
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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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