Solving a Constrained Optimization Problem by Substitution
The substitution method is a technique used to solve constrained optimization problems. A common application involves using the optimality condition, such as MRS = MRT, to establish one equation, and using the constraint (e.g., the budget constraint) as a second equation. This resulting system of two equations can then be solved by substituting one into the other to find the optimal values of the variables. Alternatively, the constraint equation can be substituted directly into the objective function (e.g., the utility function) to create a new function of a single variable, which can then be optimized using calculus.
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