4. A firm can produce a quantity q(x, y) ((x + 1)³+y³)¹/3, in kg, of its good when it uses rkg of copper and ykg of iron. If copper and iron cost r and s pounds per kg respectively, use the method of Lagrange multipliers to find the bundle of copper and iron that will minimise this firm's costs if it has to produce Qkg of its good. [You are not required to justify the use of the method of Lagrange multipliers here.] Also find this firm's minimum cost, C(Q), and verify that C'(Q) is equal to the value of the Lagrange multiplier. In what ratio should this firm decrease the amount of copper and iron in their optimal bundle if they want to obtain the greatest decrease in their cost?

4. A firm can produce a quantity q(x, y) ((x + 1)³+y³)¹/3, in kg, of its good when it uses rkg of copper and ykg of iron. If copper and iron cost r and s pounds per kg respectively, use the method of Lagrange multipliers to find the bundle of copper and iron that will minimise this firm's costs if it has to produce Qkg of its good. [You are not required to justify the use of the method of Lagrange multipliers here.] Also find this firm's minimum cost, C(Q), and verify that C'(Q) is equal to the value of the Lagrange multiplier. In what ratio should this firm decrease the amount of copper and iron in their optimal bundle if they want to obtain the greatest decrease in their cost?

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

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