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A firm uses wool and cotton fiber to produce cloth. The amount of cloth produced is given by f(x, y) = xy – x – y – 1 where x is the amount of cotton (in lbs.) and y is the amount of wool (in lbs.). Cotton costs $1.00 per pound and wool costs $3.00 per pound. The firm has $1000 to spend on fiber. Use Lagrange multipliers to determine how much cotton and how much wool the firm should by to maximize the amount of cloth they can produce, i.e. use Lagrange multipliers to find the critical point.

A firm uses wool and cotton fiber to produce cloth. The amount of cloth produced is given by f(x, y) = xy – x – y – 1 where x is the amount of cotton (in lbs.) and y is the amount of wool (in lbs.). Cotton costs $1.00 per pound and wool costs $3.00 per pound. The firm has $1000 to spend on fiber. Use Lagrange multipliers to determine how much cotton and how much wool the firm should by to maximize the amount of cloth they can produce, i.e. use Lagrange multipliers to find the critical point.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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A firm uses wool and cotton fiber to produce cloth. The amount of cloth produced is given by \( f(x, y) = xy - x - y - 1 \) where \( x \) is the amount of cotton (in lbs.) and \( y \) is the amount of wool (in lbs.). Cotton costs $1.00 per pound and wool costs $3.00 per pound. The firm has $1000 to spend on fiber. Use Lagrange multipliers to determine how much cotton and how much wool the firm should buy to maximize the amount of cloth they can produce, i.e., use Lagrange multipliers to find the critical point.
Transcribed Image Text:A firm uses wool and cotton fiber to produce cloth. The amount of cloth produced is given by \( f(x, y) = xy - x - y - 1 \) where \( x \) is the amount of cotton (in lbs.) and \( y \) is the amount of wool (in lbs.). Cotton costs $1.00 per pound and wool costs $3.00 per pound. The firm has $1000 to spend on fiber. Use Lagrange multipliers to determine how much cotton and how much wool the firm should buy to maximize the amount of cloth they can produce, i.e., use Lagrange multipliers to find the critical point.
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