Lesson 2

We can also encode the score by adding a second variable: \[ F(x,y)=(1+x^2y^1)(1+x^3y^4)(1+x^5y^5)(1+x^7y^6). \] 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 \[ \max\{r \colon \text{there exists }b\le B\text{ such that }[x^b y^r]F(x,y)>0\}. \]