You have been given an internship at the extremely profitable and secretive bank HG Fargo

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You have been given an internship at the extremely profitable and secretive bank HG Fargo. Your immediate supervisor tells you that higher-ups in the bank are very interested in learning from the past. In particular, they want to know how much money they could have made if they had invested optimally.

Your supervisor gives you the following data on the prices1 of select stocks in 2010 and in 2021:

 

 

As a first step, you decide to examine what the optimal decision is for a couple of small examples:

(a)  If you had $20 available to purchase stocks in 1991, how much of each stock should you have bought to maximize profits when you sell everything in 2011?Note that you do not need to invest all of your money — if it is more profitable to keep some as cash, you do not need to invest it.

(b)  If you had $30 available to purchase stocks in 1991, how much of each stock should you have bought?

(c)  If you had $120 available to purchase stocks in 1991, how much of each stock should you have bought?