The mathematical model that combines the factors of circumstance and a goal to determine the number resources needed to attain the goal is best described as:

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The Queuing Theory is a mathematical model used to predict queue lengths and waiting times in systems, essentially combining factors of circumstance (such as arrival rates of customers) and a goal (such as minimizing waiting time) to determine the number of resources (like servers or service channels) needed to attain that goal.

The Mathematical Model That Combines the Factors of Circumstance and a Goal