The following example illustrates the use of the substitution method and the method of Lagrange multipliers for solving a nonlinear programming problem.
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
20 x 1 + 10 x 2 = 800 bd. ft.
Determine the Excel solution to this model.