Question

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 andA 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 Eof 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.

Answer 1

2 H+3ao(tto, d2A) >↑/h@oo(14o.o2A] 2 > 300ヒ 30o 2 ,le < . 63으.2/ → = 21300