Introduction In the popular computer game League of Legends, aplayer’s Effective Health, E, when defending against physicaldamage is given by E = H(1 + 0.02A) where H and A denote theplayer’s chosen units of health and armor, respectively.Furthermore, a unit of health costs 4 gold pieces and a unit ofarmor costs 24 gold pieces. If you have 3,600 gold pieces to spendand you need to maximise the effectiveness E of your health andarmor to survive as long as possible against enemy attacks, howmuch of each should you buy?
A1. (1 mark) Write down the Lagrange function associated withthis optimisation problem.
A2. Solve the problem using the Lagrange Multipliermethod (show your work).
A3. Thirty minutes into the game, you have 2,000health and 40 armor. You have 1,800 gold pieces to spend, and againhealth costs 4 gold per unit and armor costs 24 gold per unit. Ifthe goal is still to maximise the effectiveness E of your resultinghealth and armor (after purchase), how much of each should you buywith your 1,800 gold pieces (show your work).
