Multi-dimensional Knapsack with Minimum Value constraints for Dimensions

In MDK, we have a vector $ W = \{W_1, W_2, …, W_d\}$ where each element corresponds to the maximum weight for the respective dimension in the knapsack.

I want to add a conditional constraint: $ V = {V_1, V_2, …, V_d}$ , where each $ i$ -th dimension in the knapsack must have a value sum greater than threshold $ V_i$ . I am not so much concerned with the total value sum.

I would like to show this problem is NP-hard. My intuition is that the additional constraint makes this problem harder than MKD and therefore is NP-hard. But clearly this doesn’t constitute a formal proof.

What are the physical dimensions of the Immovable Rod?

In our recent campaign came across an Immovable Rod.

Its official description states:

This flat iron rod has a button on one end. You can use an action to press the button, which causes the rod to become magically fixed in place. Until you or another creature uses an action to push the button again, the rod doesn’t move, even if it is defying gravity. The rod can hold up to 8,000 pounds of weight. More weight causes the rod to deactivate and fall. A creature can use an action to make a DC 30 Strength check, moving the fixed rod up to 10 feet on a success.

There are no physical dimensions in regards to size and weight given (e.g. is it a 500mm bar that weighs 1 kg?).

Is there any official description of the physical dimensions of the Immovable Rod, or is it up to the DM’s discretion?

Does changing the outside dimensions of a Bag of Holding break anything mechanically?

One of my players made a character who’s a 2ft. tall gnome artificer. He just created a bag of holding as his wondrous invention, but the exterior dimensions (2ft. wide by 4ft. deep) is bigger than him. So I decide to make it a drawstring backpack with a 2ft. mouth so he still has the same insertion dimensions, and 1.5ft. deep so he can wear it like a backpack and not trip.

Does this change anything about the bag mechanically? Does this seem like a reasonable change?

What are the dimensions of a box that can contain 20 arrows?

I am playing a level 13 Fighter with the Sharpshooter martial archetype (from Unearthed Arcana: Fighter). I took the Sharpshooter feat as well, of course, and the Archery fighting style. I shoot between 3 and 6 arrows per round (using Action Surge and Extra Attack), so I need a lot of arrows to keep me going through combat.

A Bag of Holding seems to be best option for holding the arrows I will need; since I read this thread, I plan on using a box to hold the bundles – presumably 1 box per bundle to keep things organized.

What dimensions would such a box need to be able to hold 20 arrows?

I am specifically asking for the dimensions of a box that can hold 20 arrows because that determines how many boxes I can put in a bag of holding, which will equal how many arrows I can safely put in a bag of holding.

Custom image dimensions for each category

Hi everyone and happy new year 2020,

I need to set up different image dimensions for each category of a website.

For example,

To set these dimensions for Category 1:

Catalog Images = 240 x 320px
Single Product Image = 470 x 627px
Product thumbnails = 75 x 100px

And these dimensions for category 2:

Catalog Images = 245 x 245px
Single Product Image = 470 x 470px
Product thumbnails = 75 x 75px

I use woocommerce.
How to do this? Is there any code or filter to affect to that a named…

Custom image dimensions for each category