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  3. 1. in league of legends, a player’s effecti

1. In League of Legends, a player’s Effective Health when defending against physical damage is given...

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Basic Math

1. In League of Legends, a player’s Effective Health whendefending against physical damage is given by E = H(100 + A)/100where H is health and A is armor. Health costs 2.5 gold per unitand Armor costs 18 gold per unit. Ten minutes into the game, youhave 1080 health and 10 armor. You have only 720 gold to spend, andthe health armor costs the same as before. Again, the goal is tomaximize the effectiveness E. Notice that you don’t want tomaximize the effectiveness of what you purchased - you want tomaximize the effectiveness E of your resulting health and armor.How much of each should you buy?

2. Thirty minutes into the game, you have 2000 health and 50armor. You have 1800 gold to spend, and again the costs are thesame. You once more want to maximize the effectiveness E of yourresulting health and armor. How much of each should you buy?

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