(*This is meant to run in Mathematica. For those who have it you presumably know how to use it. For those who don't, simply copy-paste this entire thing into it and change what you need to change. (The appropriate spots have been specified). Then simply select everything (Ctrl+A) and execute (Shift+Enter). For anybody who's interested, I hope this is helpful to you.*) Clear["Global`*"] (*Ingredients list*) (*Each ingredient is in the format of "name, magimins, traits". The \ magimins are defined in-game as A,B,C,D,E. E.g. the feyberry has 6 \ parts of magimin A and 0 of B,C,D,E*) ingredients = { {"feyberry", {6, 0, 0, 0, 0}, {0, 0, 0, 0, 0}}, {"mandrake_root", {0, 6, 0, 0, 0}, {0, 0, 0, 0, 0}}, {"sack_of_slime", {0, 0, 6, 0, 0}, {0, 0, 0, 0, 0}}, {"pixiedust_diamond", {0, 4, 4, 0, 0}, {0, 0, 0, 0, 0}}, {"unicorn_horn", {0, 0, 8, 0, 0}, {-1, 0, 0, 0, 0}}, {"rotfly_larva", {0, 0, 4, 0, 0}, {1, 0, 0, 0, 0}}, {"river-pixie's_shell", {4, 4, 0, 0, 0}, {0, 0, 0, 0, 0}}, {"leech_snail's_shell", {12, 12, 0, 0, 0}, {0, 0, 0, 0, 0}}, {"horned_jelly", {18, 0, 0, 0, 0}, {0, -1, 0, 1,0}}, {"sphinx_flea", {12, 6, 0, 0, 0}, {0, 1, 0, 0, 0}}, {"kappa_pheromones", {4, 0, 4, 0, 0}, {0, 0, 0, 0, 0}}, {"cubic_ooze", {3, 3, 3, 0, 0}, {0, 0, 0, 0, 0}}, {"fairy_flower_bulb", {4, 0, 0, 0, 0}, {0, 0, 1, 0, 0}}, {"river_calamari", {8, 0, 0, 0, 0}, {0, -1, 0, 0, 0}}, {"glass_ore", {0, 0, 0, 18, 0}, {0, 0, 0, 0, 0}}, {"serpent's_slippery_tongue", {0, 8, 0, 0, 0}, {0, 0, -1, 0,0}}, {"rotfly_cocoon", {0, 0, 12, 0, 0}, {1, 0, 0, 0, 0}},{"sack_of_hive_slime", {0, 0, 18, 0, 0}, {0, 0, 0, 0,0}}, {"bog_beet", {0, 27, 0, 0, 0}, {-1, 0, 0, 0, 1}}, {"qilin's_tri_horn", {0, 0, 24, 0, 0}, {-1, 0, 0, 0, 0}}, {"bubble_ooze", {9, 9, 12, 12, 0}, {0, 0, 0, 0, 0}}, {"golem's_eye_diamond", {0, 12, 12, 0, 0}, {0, 0, 0, 0, 0}}, {"manwyrm_root", {0, 18, 0, 0, 0}, {0, 0, 0, 0, 0}}, {"figment_pomme", {0, 18, 6, 0, 0}, {0, 0, 0, 0, 0}}, {"golemite", {18, 12, 0, 10, 0}, {0, 0, 0, 0, 0}}, {"puckberry", {18, 0, 0, 0, 0}, {0, 0, 0, 0, 0}}, {"warg_pheromones", {12, 0, 12, 0, 0}, {0, 0, 0, 0, 0}}, {"murkwater_pearl", {0, 0, 0, 12, 0}, {0, 0, 0, 1, 0}}, {"swamp_fish", {12, 0, 0, 6, 0}, {0, 0, 0, 0, 0}}, {"fairy_flower_bud", {12, 0, 0, 0, 0}, {0, 0, 1, 0, 0}}, {"impstool_mushroom", {0, 4, 0, 0, 0}, {0, 1, 0, 0, 0}}, {"mud_shrimp", {6, 0, 12, 0, 0}, {0, 0, 1, 0,0}}, {"desert_metal", {0, 12, 0, 0, 0}, {0, 1, 0, 0, 0}}, {"antlered_jelly", {30, 0, 0, 0, 0}, {0, -1, 0, 1, 0}}, {"static_spiderling", {0, 0, 0, 0, 30}, {0, 0, 0, -1, 1}}, {"cobweb_crayfish", {10, 0, 20, 0, 0}, {0, 0, 1, 0, 0}}, {"hallucinatory_shroom", {0, 0, 30, 0, 0}, {1, 0, 0, 0, -1}}, {"phantom_pomme", {0, 10, 30, 0, 0}, {1, 0, 0, 0, -1}}, {"mandragon_root", {0, 30, 0, 0, 0}, {0, 0, 0, 0, 0}}, {"barghast_canine", {0, 30, 0, 0, 10}, {0, 0, 0, 0, 0}}, {"spriggan_antler", {0, 0, 40, 0, 0}, {-1, 0, 0, 0, 0}}, {"mote_of_mana", {15, 15, 15, 15, 15}, {0, 0, 0, 0, 0}}, {"thunderbird's_molted_feather", {0, 0, 30, 0, 10}, {0, 0, 0, 0, 0}}, {"fire_flower", {40, 0, 0, 20, 0}, {0, 0, -1, 0, 0}}, {"fulgurite_ore", {0, 0, 0, 30, 0}, {0, 0, 0, 0, 0}}, {"slapping_turtle's_shell", {20, 20, 0, 0, 0}, {0, 0, 0, 0, 0}}, {"raiju_droppings", {0, 0, 30, 10, 0}, {0, 0, 0, 0, 0}}, {"thunder_quartz", {30, 10, 20, 0, 0}, {0, 0, 0, 0, 0}}, {"bogeyberry", {30, 0, 0, 0, 0}, {0, 0, 0, 0, 0}}, {"saltwatermelon", {0, 0, 0, 40, 0}, {0, 0, 0, -1, 0}}, {"reef_radish", {0, 30, 0, 0, 0}, {-1, 0, 0, 0, 1}}, {"rotfly_adult", {0, 0, 20, 0, 0}, {1, 0, 0, 0, 0}}, {"malachite_ore", {30, 10, 0, 0, 20}, {0, 0, 0, 0, 0}}, {"sack_of_composite_slime", {0, 0, 30, 0, 0}, {0, 0, 0, 0, 0}}, {"dropsider's_shadow", {0, 0, 30, 20, 10}, {0, 0, 0, 0, 0}}, {"ghostlight_bloom", {18, 0, 0, 6, 0}, {0, 0, 0, 0, 0}}, {"squid_vine", {20, 20, 15, 0, 15}, {0, 0, 0, 0, 0}}, {"mosquito_plant", {10, 0, 20, 0, 30}, {0, 0, 0, 0, 0}}, {"fairy_flower_bloom", {20, 0, 0, 10, 0}, {0, 0, 1, 0, 0}}, {"spider's_bait_diamond", {0, 20, 20, 0, 0}, {0, 0, 0, 0, 0}}, {"sea_salt", {30, 0, 0, 0, 10}, {0, 0, 0, 0, 0}}, {"dwarf_kraken", {40, 0, 0, 0, 0}, {0, -1, 0, 0, 0}}, {"nessie_pheromones", {20, 0, 20, 0, 0}, {0, 0, 0, 0, 0}}, {"selkie_lice", {10, 20, 0, 0, 0}, {0, 1, 0, 0, 0}}, {"banshee's_bloody_tongue", {0, 40, 0, 0, 0}, {0, 0, -1, 0, 0}}, {"abyssalite", {30, 20, 0, 0, 10}, {0, 0, 0, 0, 0}}, {"giantstool_mushroom", {0, 20, 0, 0, 0}, {0, 1, 0, 0, 0}}, {"photonic_spore", {0, 10, 0, 30, 0}, {-1, 0, 1, 0, 0}}, {"miasma_spore", {0, 18, 0, 6, 0}, {0, 0, 0, 0, 0}}, {"shadowveil_pearl", {0, 0, 0, 20, 0}, {0, 0, 0, 1, 0}}, {"electrocution_eel", {10, 10, 10, 0, 0}, {0, 0, 0, 1, 0}}, {"copper_dollop", {15, 15, 15, 15, 0}, {0, 0, 0, 0, 0}}, {"shelled_pudding", {32, 0, 0, 32, 0}, {0, 0, 0, 0, 0}}, {"rock_salt", {24, 0, 0, 0, 8}, {1, 0, 0, 1, 0}}, {"watchdog_daisy", {0, 16, 0, 48, 0}, {0, 0, 0, 0, 0}}, {"owlbear_pheromones", {0, 0, 0, 0, 64}, {0, 0, -1, 0, 0}}, {"naga's_fang", {0, 48, 0, 0, 16}, {0, -1, 0, 0, 1}}, {"weeping_metal_ore", {0, 32, 64, 0, 0}, {0, -1, 0, 0, 0}}, {"sepulcher_widow", {0, 0, 0, 0, 48}, {0, 0, 0, -1, 1}}, {"crag_crab", {0, 0, 0, 0, 32}, {0, 0, 1, 0, 0}}, {"griffin's_whetstone_diamond", {0, 32, 32, 0, 0}, {0, 0, 0, 0, 0}}, {"medusa_spore", {0, 48, 0, 16, 0}, {-1, 0, 1, 0, 0}}, {"harpy's_heart_of_stone", {16, 0, 0, 32, 0}, {0, 1, 0, 0, 0}}, {"feathered_gelatin", {0, 0, 0, 48, 0}, {0, 1, -1, 0, 0}}, {"scimitar_crab's_shell", {32, 32, 0, 0, 0}, {0, 0, 0, 0, 0}}, {"sequined_custard", {0, 0, 32, 0, 16}, {0, 0, 0, 1, 0}}, {"swamp_octopus", {24, 0, 0, 0, 0}, {0, -1, 0, 0, 0}} }; MatrixForm[ingredients]; (*Potion list and ratios*) (*The ratio is interpreted as the proportios of each magimin. E.g. a \ health potion with a total value of 10, would need 5 of A, 5 of B and \ 0 from C,D,E to be considered an excellent potion*) potions = { {"health_potion", {1, 1, 0, 0, 0}}, {"mana_potion", {0, 1, 1, 0, 0}}, {"stamina_potion", {1, 0, 0, 0, 1}}, {"speed_potion", {0, 0, 1, 1, 0}}, {"fire_tonic", {1, 0, 1, 0, 0}}, {"ice_tonic", {1, 0, 0, 1, 0}}, {"thunder_tonic", {0, 1, 0, 1, 0}}, {"shadow_tonic", {0, 1, 0, 0, 1}}, {"sight_enhancer", {3, 4, 3, 0, 0}}, {"alertness_enhancer", {0, 3, 4, 3, 0}}, {"insight_enhancer", {4, 3, 0, 0, 3}}, {"dowsing_enhancer", {3, 0, 0, 3, 4}}, {"poison_cure", {2, 0, 1, 1, 0}}, {"drowsiness_cure", {1, 1, 0, 2, 0}}, {"petrification_cure", {1, 0, 2, 0, 1}}, {"silence_cure", {0, 2, 1, 0, 1}} }; MatrixForm[potions]; (*Cauldron constraints*) (*The size is how many ingredients can fit in cauldron, the maxValue \ is the total amount of magimins that fit in the cauldron*) cauldronSize = 8; cauldronMaxValue = 405; (*Chosen Potion and Trait set*) (*chosenPotion is the potion you want to make*) (*chosenTrait is what traits you want that potion to have. These are \ defined as 1="good", -1="bad" and 0="I don't care"*) chosenPotion = {"shadow_tonic", {0, 1, 0, 0, 1}}; chosenTrait = {0, 0, 1, 0, 1}; (*Ingredients for chosen potion*) (*These are the appropriate ingredients based on their magimins*) truthfulness = ConstantArray[False, {Length[ingredients], 5}]; For]], i++,
For[k = 1, k <= Length[ingredients], k++,
If[chosenPotion[[2]][[i]] != 0,
If[ingredients[[k, 2]][[i]] >= 0,
truthfulness[[k, i]] = True,
truthfulness[[k, i]] = False
],
If[ingredients[[k, 2]][[i]] != 0,
truthfulness[[k, i]] = False,
truthfulness[[k, i]] = True
]
];
];
];[/code]

acceptableIngredients = Array[0, {Length[ingredients], 3}]; For[j = 1, j <= Length[ingredients], j++, If[truthfulness[[j]] == {True, True, True, True, True}, acceptableIngredients[[j]] = {ingredients[[j, 1]], ingredients[[j, 2]], ingredients[[j, 3]]}, acceptableIngredients[[j]] = {0, 0, 0} ]; ]; MatrixForm[acceptableIngredients]; (*Trait constraint*) (*These are the appropriate ingredients based on their traits*) traitConstraints = ConstantArray[False, {Length[ingredients], Length[chosenTrait]}]; For, i++,
For[k = 1, k <= Length[ingredients], k++,
If[chosenTrait[[i]] == 1,
If[ingredients[[k, 3]][[i]] == 1 ||
ingredients[[k, 3]][[i]] == 0 ,
traitConstraints[[k, i]] = True,
False],
If[chosenTrait[[i]] == 0,
If[
ingredients[[k, 3]][[i]] == 1 ||
ingredients[[k, 3]][[i]] == 0 ||
ingredients[[k, 3]][[i]] == -1,
traitConstraints[[k, i]] = True],
If[chosenTrait[[i]] == -1,
If[
ingredients[[k, 3]][[i]] == -1 ||
ingredients[[k, 3]][[i]] == 0 ,
traitConstraints[[k, i]] = True,
False];
] ] ]; ]; ];

acceptableTraits = ConstantArray[0, Length[ingredients]];
For, i++,
If[traitConstraints[[i]] == {True, True, True, True, True},
acceptableTraits[[i]] = {True, True, True, True, True},
acceptableTraits[[i]] = {False, False, False, False, False}]
];

MatrixForm[acceptableTraits];

(*True ingredients*)
(*These are all the appropriate ingredients based on their magimins AND traits*)
trueIngredients = ConstantArray[0, {Length[ingredients], 3}];
For, i++,
If[acceptableIngredients[[i, 1]] != 0 &&
acceptableTraits[[i]] == {True, True, True, True, True},
trueIngredients[[i]] = {ingredients[[i, 1]], ingredients[[i, 2]],
ingredients[[i, 3]]},
trueIngredients[[i]] = {0, 0, {0, 0, 0, 0, 0}}
] ];

MatrixForm[trueIngredients];

(*These variables x represent the quantity of each \
ingredient in the final potion*)
variables = Array[x, Length[trueIngredients]];

In[163]:= (*Sum defines the total amount of each magimin category \
(A,B,C,D,E) in the final potion*)
sum = ConstantArray[0, 5];

For[j = 1, j <= 5, j++,
For, i++,
If[Total[trueIngredients[[i, 2]]] != 0,
sum[[j]] += trueIngredients[[i, 2]][[j]]*variables[[i]]
]; ]; ];

MatrixForm[sum];

(*These are the required ingredients, at least one which is needed to end up with a potion with the appropriate traits*)
(*Pos gives us the position of each of those required ingredients in \
the trueIngredients list*)
required = Array[0, Length[chosenTrait]];
posit = Array[0, Length[required]];
pos = Array[0, Length[required]];
For, i++,
If[chosenTrait[[i]] == 1,
required[[i]] =
Select[trueIngredients, #[[3]][[i]] == chosenTrait[[i]] &];
posit[[i]] =
Flatten[Position[trueIngredients, #] & /@ required[[i]]];
pos[[i]] = variables[[posit[[i]]]]
]; ];

MatrixForm[required];

MatrixForm[pos];


post = Array[1, Length[chosenTrait]];
For, i++,
If[Depth[pos[[i]]] == 2,
post[[i]] = 1,
post[[i]] = Total[pos[[i]]]
] ]

For, i++,
If[post[[i]] == 1,
post[[i]] = 1
] ];

MatrixForm[post];

(*Formulate the optimization problem*)
(*Here we define all the constraints of our problem*)
constraints = {
Total[Total[trueIngredients[[All, 2]]*variables]] <= cauldronMaxValue,
Total[variables] <= cauldronSize,
sum[[1]] <= (chosenPotion[[2]][[1]]/Total[chosenPotion[[2]]])*
Total[Total[trueIngredients[[All, 2]]*variables]],
sum[[2]] <= (chosenPotion[[2]][[2]]/Total[chosenPotion[[2]]])*
Total[Total[trueIngredients[[All, 2]]*variables]],
sum[[3]] <= (chosenPotion[[2]][[3]]/Total[chosenPotion[[2]]])*
Total[Total[trueIngredients[[All, 2]]*variables]],
sum[[4]] <= (chosenPotion[[2]][[4]]/Total[chosenPotion[[2]]])*
Total[Total[trueIngredients[[All, 2]]*variables]],
sum[[5]] <= (chosenPotion[[2]][[5]]/Total[chosenPotion[[2]]])*
Total[Total[trueIngredients[[All, 2]]*variables]],
post[[1]] >= 1,
post[[2]] >= 1,
post[[3]] >= 1,
post[[4]] >= 1,
post[[5]] >= 1,
variables \[Element] PositiveIntegers
};

(*Solve the optimization problem*)
solution = NMaximize[{Total[Total[trueIngredients[[All, 2]]*variables]],
constraints}, variables];

(*Display the result*)
ingredientQuantities = variables /. solution[[2]];

(*Extract the names of the ingredients needed for the potion*)
neededIngredients = Select[Transpose[{trueIngredients[[All, 1]],
ingredientQuantities}], #[[2]] > 0 &];

If[solution[[1]] >= 1 && solution[[1]] <= 60,
class = "minor",
If[solution[[1]] > 60 && solution[[1]] <= 150,
class = "common",
If[solution[[1]] > 150 && solution[[1]] <= 290,
class = "greater",
If[solution[[1]] > 290 && solution[[1]] <= 470,
class = "grand",
class = "masterwork"
] ] ] ];

If[AnyTrue[required, #[[All]] == {} &],
solution[[1]] = 0;
];

If[solution[[1]] > 0,
Print["The ingredients needed to make a '", class, " ",
chosenPotion[[1]], "' with a ", chosenTrait,
" trait set and a total value of ", solution[[1]], " are:"];
Print[neededIngredients];,
Print["There is no viable set of ingredients to create a perfectly \
balanced '", chosenPotion[[1]], "' with a ", chosenTrait,
" trait set."];
];
[/code]