Question

In: Advanced Math

Introduction In the popular computer game League of Legends, a player’s Effective Health, E, when defending...

Introduction In the popular computer game League of Legends, a player’s Effective Health, E, when defending against physical damage is given by E = H(1 + 0.02A) where H and A denote the player’s chosen units of health and armor, respectively. Furthermore, a unit of health costs 4 gold pieces and a unit of armor costs 24 gold pieces. If you have 3,600 gold pieces to spend and you need to maximise the effectiveness E of your health and armor to survive as long as possible against enemy attacks, how much of each should you buy?

A1. (1 mark) Write down the Lagrange function associated with this optimisation problem.

A2. Solve the problem using the Lagrange Multiplier method (show your work).

A3. Thirty minutes into the game, you have 2,000 health and 40 armor. You have 1,800 gold pieces to spend, and again health costs 4 gold per unit and armor costs 24 gold per unit. If the goal is still to maximise the effectiveness E of your resulting health and armor (after purchase), how much of each should you buy with your 1,800 gold pieces (show your work).

Solutions

Expert Solution

1) Given that :

In the popular computer game League of Legends, a player’s Effective Health, E, when defending against physical damage is given by E = H(1 + 0.02A) where H and A denote the player’s chosen units of health and armor, respectively. Furthermore, a unit of health costs 4 gold pieces and a unit of armor costs 24 gold pieces. If you have 3,600 gold pieces to spend and you need to maximise the effectiveness E of your health and armor to survive as long as possible against enemy attacks

ans:

Let us assume that you buy  units of health.

Therefore you can buy

(assuming you would like to spend your entire money).

And the effective health is :

We want to maximize this function. Since the coefficient of is negative, the point which we have a zero derivative, we have a maxima. We find that the derivative is 0 at the point .

So you should buy 600 units of health and 50 units of armor.

2) Given that :

Thirty minutes into the game, you have 2,000 health and 40 armor. You have 1,800 gold pieces to spend, and again health costs 4 gold per unit and armor costs 24 gold per unit. If the goal is still to maximise the effectiveness E of your resulting health and armor (after purchase)

ans :

Again if  denotes the number of health units bought, we have

units of armor.

The effective health in this case is :

Again at the point at which derivative is zero is the point of maxima. But this time we have a derivative 0 at point . Since have to non negative units of health, we have to maxima when .

But after the point   the quadratic is strictly decreasing. Hence the maximum is at point

. Hence we should buy 0 unit of health and 75 units of armor.


Related Solutions

Introduction In the popular computer game League of Legends, a player’s Effective Health, E, when defending...
Introduction In the popular computer game League of Legends, a player’s Effective Health, E, when defending against physical damage is given by E = H(1 + 0.02A) where H and A denote the player’s chosen units of health and armor, respectively. Furthermore, a unit of health costs 4 gold pieces and a unit of armor costs 24 gold pieces. If you have 3,600 gold pieces to spend and you need to maximise the effectiveness E of your health and armor...
1. In League of Legends, a player’s Effective Health when defending against physical damage is given...
1. In League of Legends, a player’s Effective Health when defending against physical damage is given by E = H(100 + A)/100 where H is health and A is armor. Health costs 2.5 gold 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....
JAVA : Design and implement an application that plays the Rock-Paper-Scissors game against the computer. When...
JAVA : Design and implement an application that plays the Rock-Paper-Scissors game against the computer. When played between two people, each person picks one of three options (usually shown by a hand gesture) at the same time, and a winner is determined. In the game, Rock beats Scissors, Scissors beats Paper, and Paper beats Rock. The program should randomly choose one of the three options (without revealing it) and then prompt for the user’s selection. At that point, the program...
Design and implement an Android application that plays the Rock-Paper-Scissors game against the computer. When played...
Design and implement an Android application that plays the Rock-Paper-Scissors game against the computer. When played between two people, each person picks one of three options (usually shown by a hand gesture) at the same time, and a winner is determined. In the game, Rock beats Scissors, Scissors beats Paper, and Paper beats Rock. The program should randomly choose one of the three options (without revealing it) and then seek for the user’s selection (using your choice of an object...
What barriers might exist to providers’ adoption of computer-based algorithms when predicting health status of patients?...
What barriers might exist to providers’ adoption of computer-based algorithms when predicting health status of patients? How could these tools and information be presented in a way to make them actionable for physicians and their care teams?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT