Question

The Oompa Loompas at Willie Wonka's Chocolate Factory are looking to maximize the factory's profits by producing desserts, but they are constrained by a fixed budget that they can spend on the different ingredients. (Assume that ingredients represent the only expense the factory has.) Charlie wants to help them figure out the best way to allocate this money and decides to solve a constrained optimization problem using the Lagrange Multiplier Method. As he writes down some equations, one of the Compa Loompas asks him what the X (.e. the Lagrange Multiplier) means. Charlie should explain that represents:

a. The optimal cost of a dessert
b. The optimal amount of money to spend on ingredients
c. The marginal profit of an increase in the budget
d. The marginal profit of a dessert produced in the factory

Answer 1

b. The Lagrange Multiplier (X) represents the optimal amount of money to spend on ingredients in a constrained optimization problem.

Step-by-step explanation:

The X (Lagrange Multiplier) in the context of a constrained optimization problem represents:

b. The optimal amount of money to spend on ingredients

The Lagrange Multiplier Method is used to solve constrained optimization problems. In this case, the Oompa Loompas at Willie Wonka's Chocolate Factory want to maximize profits by producing desserts while staying within a fixed budget for ingredients. The Lagrange Multiplier (X) helps determine the optimal amount of money to spend on ingredients that will maximize profits while staying within the budget constraint.