Which of the following statements is not one of the benefits of mathematical models? The first one is “theorems are axiomatic.” The second one is “models are mathematically adequate.” The third one is “there are no unknown unknowns.”

We shall see these three statements again in the literature. Let’s start with the first one: “models are mathematically adequate.” The entire point of doing any modeling, whether it is a technical problem or a developmental problem, is to assume certain values and use them to approximate another set of results. If the models can be used to approximate a range of outcomes, then they are sufficiently accurate and can be called approximate. (There are times when they are not, like when using the polynomial kind of modeling process for solving systems of logistic regression that assumes a normal distribution.)

## Evaluating A Mathematical Model

Here is another example: “The greatest asset a company can have is a predictable and consistent lead time.” This sounds like an obvious result, but it isn’t as obvious as it sounds when you factor in all of the factors that go into determining lead time. To take just one example, suppose that the lead time is two months. What if a couple of weeks go by without an order? It could still be considered relatively fast, but it isn’t very predictable.

Let us return to our statement about having a predictable and consistent lead time. This implies that there is some sort of measure, such as a mean or an arithmetic mean, that changes over time. But what do we mean by “a mean” here? Well, we could say that there is some kind of difference between the initial value of any variable and the actual value after a certain number of changes have been made, such as adding new data to a spreadsheet, or subtracting data from the spreadsheet. In other words, the mean is a statistical constant used to measure the probability that the mean will change over time, and it gives us the probability that changes will take place.

The meaning of “the mean” could be different depending on which way you think of it. For instance, it might mean the difference between the final value of the dependent variable and the corresponding value for the independent variable. For our example, the value of a.5 can be compared to the value of a.5 at the end of July, which would be the value of a.5 at the end of August, the value of a.5 at the end of September, and so on. In this example, the term “the mean” is used to denote the uniform probability that the dependent variable, the average price, changes over time, while the term “the uniform distribution” denotes the probability that the decision variables, individual prices, change uniformly over time.

## These Are The Advantages Of Mathematical Models

One of the advantages of mathematical models is that they are deterministic or stochastic. This means that their results are repeatable; that is, the same results will always occur even if the inputs to the system change. In the case of the pricing constraint, the objective function and the decision variables can be set equal in initial conditions so that the same price will always be expected. In this kind of model, the distribution of returns, or the distribution of utility, is different from the normal distribution because its mean is different and can be characterized by a distinct shape.

If we know what the mean and the decision variables should be, we can solve a more difficult problem. A cubic equation can solve an optimization problem, but the best models do not use them. The best mathematical models exhibit geometric intuition, and they solve optimization problems in a generic way. Some of the characteristics of geometric intuition are: it simplifies the problem, it is algebraically simple, and it generates solutions independent of inputs. Which of the following is not one of advantages of mathematical models?

The second advantage is that it generates output estimates that can be compared with other models. For example, a finite difference model could output an estimate of the area of effect for the optimization problem at hand. Which of the following is not one of advantages of mathematical models?