Lesson 2

We can also encode the score by adding a second variable: \[F(x,y)=(1+x^{2}y^{1})(1+x^{3}y^{4})(1+x^{5}y^{5})(1+x^{7}y^{6}).\] Now the coefficient \([x^{b} y^{r}]F(x,y)\) is the number of portfolios with price \(b\) and score \(r\). The best score under budget \(B\) is \[\max\{r:\text{there exists }b\le B\text{ such that }[x^{b} y^{r}]F(x,y)>0\}.\]