What has Maximize been thinking about for so long?

The command

Maximize[{Sqrt[2 x + 13] + (3 y + 5)^(1/3) + (8 z + 12)^(1/4), x + y + z == 3&&{x,y,z} >= 0}, {x, y, z}] 

is running without any response on my comp for hours (as well as many other Mathematica commands). This optimization problem is quite standard and easily solved by Lagrange multipliers

L=Sqrt[2x+13]+(3y+5)^(1/3)+(8z+12)^(1/4)-t*(x+y+z-3); 

For simplicity the conditions {x,y,z}>=0 are not taken into account.

Reduce[D[L, x] == 0 && D[L, y] == 0 && D[L, z] == 0 && D[L, t] == 0, {x, y, z, t}, Reals] 

x == 3/2 && y == 1 && z == 1/2 && t == 1/4

The Hessian of L at this point is easily found by

M = {{D[L, x, x], D[L, x, y], D[L, x, z], D[L, x, t]}, {D[L, y, x],  D[L, y, y], D[L, y, z], D[L, y, t]}, {D[L, z, x], D[L, z, y],  D[L, z, z], D[L, z, t]}, {D[L, t, x], D[L, t, y], D[L, t, z],  D[L, t, t]}} /. {x -> 3/2, y -> 1, z -> 1/2, t -> 1/4} 

Next, the result of

Resolve[ForAll[{a,b,c,d}, ({a,b,c,d}.M).{a,b,c,d} <= 0], PositiveReals] 

True

states this is the maximum point (local and global) since the quadratic form ({a,b,c,d}.M).{a,b,c,d} takes nonpositive values on the positive reals. Is there anoter way to symbolically solve this optimization problem?

What is the best 2nd level spell to concentrate on to maximize damage?

In a party full of crowd control, the Magus wishes to dish out as much damage as possible. What concentration spell will allow them to do that, under the given circumstance:

  • The Magus is 4th level, any race, any class/multiclass, feats available
  • The damage is dealt out over 1 minute maximum
  • The rest of the party is focused on their own goals, so any preparation or buffs on the Magus will have to come from themselves: (no time limit)
  • Assume things go perfectly 100% of the time: ie enemies will always fail on saving throws, the Magus will always succeed on an attack roll, disregard advantage and disadvantage
  • The only source of damage tracked comes from the Magus’ concentration spell; no need to worry about ensuring their action is free every round to cast another damaging spell
  • Assume all damage is average: 1d6 = 3.5 damage, don’t round
  • If a spell can hit multiple targets, there are 2 available each round
  • These 2 enemies behave optimally for your damage: if an enemy must end its turn in the spells area to take its damage, then 2 enemies in a round will do so.

how could you maximize food production with magic items and spells over a long period of time?

Over the course of years, how would you appropriately maximize food production for a town or city? If you assume the small city/large town and its very large (100-mile radius) surrounding area can be created with this goal in mind, what spells and magic items could be useful? This should be ruling out spells that are very small individual buffs(Haste, Enlarge/Reduce etc). These options should be more efficient than Plant Growth unless they are lower level/repeatable. Creative options like the Decanter of Endless Water and similar would also be helpful!

I am asking this as a player: the premise is creating a city. Any spells are acceptable, lower magic is preferred(1-5), but higher-level options are also good to know. This question has a broader application than this related question that is only about the plant growth spell’s applicability.

Does Sword of Sharpness’s maximize damage rule apply to a Rogue’s Sneak Attack damage? [duplicate]

If a rogue hits someone with a scimitar of sharpness and the preconditions for sneak attack are in place, does the rogue also get to maximize the damage of sneak attacks?

For reference the Sword of Sharpness states:

When you attack an object with this magic sword and hit, maximize your weapon damage dice against the target. […]

How does Maximize Spell Like ability feat affect items that boost your damage?

Assume a level 9 warlock has following damage dice:

-5d6 from base EB

-2d6 from Mortalbane (Feat, does not require CL)

-2d6 from Greater Chasuble of Fell Power (Item – Caster level 9th)

-2d6 from gloves of eldritch admixture (Item – Caster Level: 3rd)

Maximize spell like ability feat mentions:

The spell-like ability you wish to maximize can be chosen only from those abilities that duplicate a spell of a level less than or equal to 1/2 your caster level (round down), minus 2.

If this warlock wanted to maximize their attack using all of the dice above, would he have to re-calculate the Maximize Spell Level according to formula [(CL/2) – 2]? If that is the case, would you take the item that requires the highest CL or add up all the spells that requires CL (1 for EB + 9 for Chasuble + 3 for the gloves)

If a player rolls 33-34 on the wild magic table (maximize damage), what happens if they miss the target on the damaging attack?

On the Wild Magic Sorcerer’s Wild Magic Table, (PHB p.104), getting a roll of 33-34 results in:

Maximize the damage of the next damaging spell you cast within the next minute.

What happens if the sorcerer casts an attack roll spell that deals damage, and misses the target? I am being confused by the term "damaging." Is a "Damaging Spell" a hidden category of spell that can be cast, and thus means casting the spell ends this effect? or does the spell need to apply damage in order to be damaging, and would therefore need to hit for the effect to happen?

If one target of a Twinned Spell has 0 HP, does the Grave cleric’s Circle of Mortality feature maximize healing on a second target who’s not at 0 HP?

One PC is a multiclassed Grave Domain cleric/sorcerer. They cast a healing spell on a PC that has 0 health, and use the Twinned Spell Metamagic option to target another PC with the same spell.

Would the second PC also have its healing from the spell maximized by the Grave cleric’s Circle of Mortality feature (XGtE, p. 20), even if the second PC is not also at 0 HP?

Best way to maximize Sneak Attack damage

Unchained Rogue

Sources allowed:

  • Core Rulebook
  • Advanced Player’s Guide
  • Advanced Class Guide
  • Advanced Race Guide
  • Ultimate Combat
  • Ultimate Magic

I’m asking for how to maximize damage output using Sneak Attack. In theory for all levels, but more specifically at level 1 through 6 or so. Whether it is using feats, magic items, (something I am overlooking?) or a combination of all of that, the objective is maximized damage output.

I don’t really want to multiclass, and want to focus on melee attacks, not ranged attacks. My character will use a shortsword.

I am just looking for maximum damage output, not how to create a ‘sneakable’ condition.