Author: haroonkhan

Inequalities like a ≤ x ≤ b, where a and b are arbitrary real numbers such that a < b, define intervals on the real line. The inequality above defines an interval that includes its extreme points. In such a case, we use the notation [a, b] to denote the interval, and we speak of a closed interval. On the contrary, inequalities a < x < b define the open interval (a, b). For…

If we order cars from a car manufacturer, we cannot order 10.56986 cars; we may order either 10 or 11 cars, but any value in between makes no sense. It should be intuitively clear what we mean by an integer number; integer numbers are used to measure variables that have a intrinsically discrete nature. A real number is…

As we have already pointed out, the reader is assumed to be equipped with a basic mathematical background about sets as well as integer and real numbers. In this section we briefly recall a few basic concepts for convenience.

In plotting the function, we have ignored the purchase cost component cd, which is constant and would just push the graph up a bit. This is not relevant to us, since what we are interested in is finding an order size Q* minimizing total cost. Indeed, since the function goes to infinity for very small and very…

Having figured out a relationship between the order size and the average total cost per year, it would be useful to plot the function in order to see the effect of Q and to figure out a good decision. There are plenty of powerful software packages that, given a range of the independent variable Q, compute the corresponding…

In order to express average total cost per unit time as a function of the order size Q, we should consider all of the factors contributing to the overall cost. The first one that comes to mind is purchase cost. If the unit item cost is c, measured in money per item, we have to pay cQ whenever…

Before getting into formal details of calculus, it is essential to arm ourselves with some motivation for doing so. In management science, we often want to relate decisions to cost or profit. This is necessary in order to find an “optimal” decision yielding the best performance in some well-specified sense. We should quote “optimal,” because…

Calculus is a classical branch of mathematics, dealing with the study of functions. A function is essentially a rule for association of one or more input variables with an output value. For instance, we might be interested in relating a decision, say, how much to produce, to the business outcome, say, profit. We have seen…