In League of Legends, a player’s Effective Health when defending against physical damage is given by: \frac{H(100+A}{100}. Where H ins health and A is armor. Health costs 2.5 per unit and Armor costs 18 gold per unit. Ten minutes into the game, you have 1080 health and 10 armor. You have only 720 gold to spend, and the health armor costs the same as before. Again, the goal is to maximize the effectiveness E. Notice that you don’t want to maximize the effectiveness of what you purchased - you want to maximize the effectiveness

E of your resulting health and armor. How much of each should you buy?

Part B:

Thirty minutes into the game, you have 2000 health and 50 armor. You have 1800 gold to spend, and

again the costs are the same. You once more want to maximize the effectiveness E of your resulting health

and armor. How much of each should you buy?