# Given the nonlinear programming model max z 5x1 2 x 2

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Chapter 11 / Exercise 57
Essential Calculus: Early Transcendentals
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35) Given the nonlinear programming model Max Z = 5x1 - 2 x 2 2 Subject to: x 1 + x 2 = 6 What is the optimal value of the Lagrange multiplier? Diff: 3
Main Heading: The Method of Lagrange Multipliers Key words: Lagrange multipliers, solution of simultaneous equations 6
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Chapter 11 / Exercise 57
Essential Calculus: Early Transcendentals
Stewart Expert Verified
36) Write the Lagrangian function for the following nonlinear program: Min x 1 2 + 2 x 2 2 - 8 x 1 - 12 x 2 + 34 subject to: x 1 2 + 2 x 2 2 = 5
37) Solve the following nonlinear program: Min x 1 2 + 2 x 2 2 - 8 x 1 - 12 x 2 + 34 subject to: x 1 2 + 2 x 2 2 = 5 Diff: 2
Main Heading: The Method of Lagrange Multipliers Key words: Lagrangian multipliers, solution 38) A customer molder produces 6-ounce juice glasses and 10-ounce cocktail glasses. The per unit contribution for the juice glasses ( x 1 ) is equal to 60 - 5 x 1 , and the per unit contribution for the cocktail glasses ( x 2 ) is 80 - 4 x 2 for a total contribution of 60 x 1 - 5 x 1 2 + 80x 2 - 4x 2 2 Demand requires that the production of juice glasses is twice the production of cocktail glasses. ( x 1 = 2 x 2 ). What is the Lagrangian function for this problem? . )
39) A customer molder produces 6-ounce juice glasses and 10-ounce cocktail glasses. The per unit contribution for the juice glasses ( x 1 ) is equal to 60 - 5 x 1 , and the per unit contribution for the cocktail glasses ( x 2 ) is 80 - 4 x 2 for a total contribution of 60 x 1 - 5 x 1 2 + 80 x 2 - 4 x 2 2 . Demand requires that the production of juice glasses is twice the production of cocktail glasses. ( x 1 = 2 x 2 ). Write the objective function for this problem which illustrates the technique of substitution. 2 Diff: 2
Main Heading: The Method of Lagrange Multipliers Key words: solution to constrained nonlinear program 7
40) The slope of a curve at its highest point equals __________. A Diff: 2
Main Heading: The Substitution Method Key words: substitution method, slope of a curve 41) The slope of a curve at any point is __________ the derivative of the curves function. C
Diff: 2 Main Heading: The Substitution Method Key words: substitution method, derivative of the function
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