Question #41685

Consider the linear programming problem: Maximize $Z = c_1 x + c_2 y$ Subject to the constraints: $x \ge 0, y \ge 0$ $x + \lambda y \le L$ $3x + 2y \le 15$ where $c_1 = \frac{2}{\binom{24}{12}} \sum_{r=0}^{12} \binom{12}{r}^2$, $c_2 = \frac{2}{\binom{24}{12}} \sum_{r=0}^{12} r \binom{12}{r}^2$, and $L = \lim_{n \to \infty} \sum_{k=1}^n \frac{40k^3}{n^4}$. If the problem has multiple optimal solutions, what is the maximum value of $Z$?