Answered: Lagrange multipliers Each function ƒ…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.4: Linear Programming

Problem 4E

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Manufacturing Calculators A manufacturer of calculators produces two models: standard and scientific. Long-term demand for the two models mandates that the company manufacture at least 100 standard and 80 scientific calculators each day. However, because of limitations on production capacity, no more than 200 standard and 170 scientific calculators can be made daily. To satisfy a shopping contract, a total of at least 200 calculators must be shipped very day. aIf the production cost is 5 for a standard calculator and 7 for a scientific one, how many of each model should be produced daily to minimize this cost. bIf each standard calculator results in a 2 loss but each scientific one produces a 5 profit, how many of each model should be made easily to maximize profit.
Manufacturing Calculators A manufacturer of calculators produces two models; standard and scientific. Long-term demand for the two models mandates that the company manufacture at least 100 standard and 80 scientific calculators each day. However, because of limitations on production capacity, no more than 200 standard and 170 scientific calculators can be made daily. To satisfy a shipping contract, A total of at least 200 calculators must be shipped every day. (a) If the production cost is $5 for a standard calculator and $7 for a scientific one, how many of each model should be produced daily to minimize this cost? (b) Id each standard calculator results in a $2 loss but each but each scientific one produces a $5 profit, how many of each model should daily to maximize profit?

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Lagrange multipliers Each function ƒ has an absolute maximum value and absolute minimum value subject to the given constraint. Use Lagrange multipliers to find these values. ƒ(x, y, z) = x - z subject to x2 + y2 + z2 - y = 2