Example Problem Solution

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The following example illustrates the use of the substitution method and the method of Lagrange multipliers for solving a nonlinear programming problem.

Problem Statement

The Hickory Cabinet and Furniture Company makes chairs and tables. The company has developed the following nonlinear programming model to determine the optimal number of chairs ( x ₁ ) and tables ( x ₂ ) to produce each day to maximize profit, given a constraint for available mahogany wood:

maximize Z = $280 x ₁ 6 x ₁ ² + 160 x ₂ 3 x ₂ ²

subject to

20 x ₁ + 10 x ₂ = 800 bd. ft.

Determine the Excel solution to this model.

Solution