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Suppose a corporation manufactures candles at two locations. The cost of producing *1units at location 1 is C₁=0.08x1² +4x1+500 and the cost of producing *2 units at location 2 is C₂=0.02x2²+4x2+350 2 The candles sell for $12 per unit. Find the quantity that should be produced at each location to maximize the profit P = 12(x₁+x2)-C₁-C₂.

Suppose a corporation manufactures candles at two locations. The cost of producing *1units at location 1 is C₁=0.08x1² +4x1+500 and the cost of producing *2 units at location 2 is C₂=0.02x2²+4x2+350 2 The candles sell for $12 per unit. Find the quantity that should be produced at each location to maximize the profit P = 12(x₁+x2)-C₁-C₂.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose a corporation manufactures candles at two locations. The cost of producing *1units at location 1 is C₁=0.08x₁² +4x1+500 and the cost of producing *2 units at location 2 is C₂ = 0.02x₂²+4x2+350 The candles sell for $12 per unit. Find the quantity that should be produced at each location to maximize the profit P = 12(x₁+x₂)-C₁-C₂. Find the partial derivatives: fx, fy, and f₂: a. f(x,y) = x5y³ In(x³ + y²) b. f(x, y, z) = x²y — 3x³ ey²-x²
Transcribed Image Text:Suppose a corporation manufactures candles at two locations. The cost of producing *1units at location 1 is C₁=0.08x₁² +4x1+500 and the cost of producing *2 units at location 2 is C₂ = 0.02x₂²+4x2+350 The candles sell for $12 per unit. Find the quantity that should be produced at each location to maximize the profit P = 12(x₁+x₂)-C₁-C₂. Find the partial derivatives: fx, fy, and f₂: a. f(x,y) = x5y³ In(x³ + y²) b. f(x, y, z) = x²y — 3x³ ey²-x²
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