Tutor profile: Matthew F.

Assign $$m$$ workers to $$n$$ tasks while minimizing the cost of the assignment.

To formulate this linear program we have: $$min \sum_i \sum_j c_{ij}x_{ij}$$ such that all workers are assigned to a job and vice versa $$\sum_{i=1}^m x_{ij}=1, \quad \forall j$$ $$\sum_{j=1}^n x_{ij}=1, \quad \forall i$$

What do eigenvalues tell you about a matrix?

In statistics, eigenvalues tell you how much variation there is in the data when doing PCA. In nonlinear optimization, positive eigenvalues indicate that a matrix is positive definite, which tells you whether or not you have a global max or min.

What is a derivative?

Derivatives tell you how fast a function is changing at a particular input value. It's also known as a rate of change. For example, $$f'(x)=\frac{d}{dx}(x^2)=2x$$. For $$x=1$$, the aforementioned function is changing at a rate of 2 units (i.e. $$f'(1)=2(1)=2$$).