I've got the following problem from an exam which shall be solved using dynamic programming and wanted to ask if the following is a valid solution: (I uploaded the tables 1-6 here: http://ibb.co/nG3YBR )
Problem:
Little Nick gets two dollars from his parents to buy sweets. With this money, he can buy Gummi bears (G) for 20c each, licorice (L) for 40c each or chocolate (C) for one dollar each. This gives him the following ADDITIONAL amounts of satisfaction: [Table 1] Obviously, he wants to maximize his satisfaction.
My Solution (the left sheet in the picture): First of all, I calculated the accumulated levels of satisfaction for each level and divided them by the price, so that I had the dimension satisfaction/money. This can be seen in table 2. Then, in a first step, I looked for the ideal "output quantity" if you would only focus on G and L. This can be seen in table 3. As an example, for an output quantity of 3, it would be best to choose 3x G, because this gives a higher level of satisfaction (375) than the other options (see diagonals; 325 and 225). In a next step, the highest levels of satisfaction for each output quantity are transferred in yet another table, where the best combination of the two elements "G&L" and C (chocolate) are determined. This gives us the ideal level of satisfaction for every output quantity. Thus, it only remains to be calculated, which of the output quantities Nick is able to afford and his optimal level of satisfaction can be determined.
However, the sample solution was different [see picture with tables 5-7]
My prof told me that my solution is invalid, as the sweets cannot be compared to each other, because they don't cost the same.
For me, it makes sense, that my table [2] cannot be completely right, because for an output quantity of 1, in the table it would not matter whether to choose G or L, whereas 2x G lead to a higher level of satisfaction than 1x L. Still, I am interested in whether it is principally feasible to solve this problem with this approach of "satisfaction per money"
Thank you so much for your help!