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The Hungarian Method is an efficient algorithm used to solve the assignment problem, where the goal is to assign tasks to agents in a way that minimizes the total cost or maximizes the total profit. The algorithm ensures that each task is assigned to exactly o...

A Restricted Assignment Problem is a variation of the classic assignment problem in which certain tasks cannot be assigned to specific agents due to constraints or limitations. These restrictions may arise due to various factors such as skill incompatibilities...

What is Linear Programming? Linear Programming (LP) is a mathematical technique used to achieve the best outcome in a given mathematical model whose requirements are represented by linear relationships. It is widely used in operations research, economics, busi...

What is Problem Formulation in Linear Programming? Linear Programming Problem Formulation refers to the process of translating a real-world problem into a mathematical model with the goal of optimizing an objective (such as maximizing profit or minimizing cost...

The Graphical Method is a visual approach to solving linear programming problems involving two decision variables. This method is limited to two-dimensional space, as it requires the problem to be represented graphically. It involves plotting the constraints a...

Introduction to the Simplex Method The Simplex Method is one of the most widely used algorithms for solving linear programming problems. Unlike the graphical method, which is limited to two variables, the Simplex Method can handle problems with multiple variab...

Linear Programming (LP) is a mathematical technique used to optimize a linear objective function, subject to a set of linear constraints. It is widely applied in operations research, economics, business, and engineering to solve optimization problems where the...

A matrix is a rectangular arrangement of numbers, symbols, or expressions, arranged in rows and columns. It is widely used in various branches of mathematics, including algebra, calculus, and statistics, as well as in applied fields like physics and computer s...

Definition The addition of matrices is the operation of adding two matrices by adding their corresponding elements. This operation is defined only for matrices of the same dimensions (i.e., they must have the same number of rows and columns). The resulting mat...

Definition The multiplication of a matrix by a scalar is an operation where every element of the matrix is multiplied by the same scalar value. A scalar is simply a constant (a real number), and when multiplying a matrix by a scalar, we apply the multiplicatio...

Definition An identity matrix is a special type of square matrix in which all the elements of the principal diagonal (from the top left to the bottom right) are equal to 1, and all other elements are 0. It is denoted as ( I ) and is known as the multiplicative...

Definition The multiplication of two matrices involves taking the rows of the first matrix and the columns of the second matrix and calculating the dot product for each pair. This operation is only defined when the number of columns in the first matrix is equa...

Matrix multiplication has several important properties that make it useful in various mathematical contexts. However, matrix multiplication differs from regular multiplication of numbers in certain aspects, such as the non-commutative property. Below are the k...

Definition The determinant is a scalar value that can be computed from the elements of a square matrix. Determinants have important applications in linear algebra, including solving systems of linear equations, finding the inverse of a matrix, and determining ...

Definition Minor The minor of an element in a matrix is the determinant of the smaller matrix that remains after removing the row and column containing that element. For any element ( a_{ij} ) in a matrix, the minor is denoted as ( M_{ij} ). Cofactor The cofac...

Definition The inverse of a matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix. Not all matrices have an inverse; a matrix must be square (having the same number of rows and columns) and have a non-zero determinant ...

Introduction Simple interest is a basic concept in commercial arithmetic used to calculate the interest earned or paid on a principal amount for a certain period of time at a specified rate of interest. It is called "simple" because the interest is calculated ...

Introduction Compound interest is a method of calculating interest where the interest earned over time is added to the principal amount, and future interest is calculated on the new total. This means that interest is earned not only on the original principal b...

Introduction The equivalent rate is a concept in commercial arithmetic used to compare different interest rates that have different compounding periods. It allows for the conversion of an interest rate compounded over one period to an equivalent interest rate ...

Introduction The effective interest rate, also known as the annual equivalent rate (AER) or effective annual rate (EAR), represents the actual interest earned or paid on a loan or investment over a year, taking into account the effect of compounding. Unlike th...