In the game of League of Legends, a player's Effective Health when defending against physical damage is given by E=100H(100+A), where H is health and A is armor. (1) Health costs 2.5 gold per unit, and Armor costs 18 gold per unit. You have 3600 gold, and you need to optimize the effectiveness, E, to survive as long as possible against the enemy team's attacks. Solve this ontimization nroblem. What is H and A at the ontimal solution? (2) Ten minutes into the game, you have 1080 health and 10 armor. You have only 720 gold to spend, and again Health costs 2.5 gold per unit while Armor costs 18 gold per unit. Again the goal is to maximize the effectiveness E. Notice that you don't want to maximize the effectiveness of what you purchase - you want to maximize the effectiveness E of your resulting health and armor. Solve this optimization problem and find the optimal H and A