A financial services company is planning its computational resource allocation for three distinct high-frequency trading algorithms over the next quarter. The company has a total of 50,000 processing hours available. Each algorithm has a unique projected profit function based on the hours it receives, and the problem is governed by the following constraints:
Algorithm A must be allocated at least 10,000 hours.
Algorithm B must be allocated no more than 25,000 hours.
The combined allocation for Algorithms A and C cannot exceed 40,000 hours. The objective is to maximize total profit, and it has been determined that both the profit functions and all constraints are linear. Which of the following methods is most suitable for determining the optimal allocation of processing hours?
The correct answer is the Simplex method. The scenario described is a classic linear programming (LP) problem, which involves optimizing a linear objective function (maximizing total profit) subject to a set of linear constraints (total hours available and specific algorithm hour limits). The Simplex method is a standard and highly effective algorithm specifically designed to solve such linear programming problems by systematically examining the vertices of the feasible region to find the optimal solution.
A greedy algorithm is incorrect because it makes locally optimal choices at each step, which does not guarantee a globally optimal solution for a problem with multiple interacting constraints. A multi-armed bandit algorithm is also unsuitable as it is designed for unconstrained problems that involve a tradeoff between exploration (trying new options) and exploitation (using known good options), not for solving a system with predefined linear constraints. Gradient descent is incorrect because it is an iterative optimization algorithm used for finding the minima of differentiable functions, which is typical for non-linear problems or for training machine learning models, not for solving linear programming problems with hard constraints.
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