## Maximize rental income given a set of date intervals

Suppose you have 1 room that you want to rent out. (AirBnb style) You want to maximize profits that you will get by renting it out.

For example: Given intervals: `[[1, 10], [2, 5], [7, 20], [23, 30]]` – you could rent it out `[2, 5], [7, 20] and [23, 30]`

Another example: `([[1, 2], [1, 11], [5, 8], [4, 33], [18, 72]])` = `66`

Note: Start and end times of the interval are inclusive

I implemented a brute force solution to this problem. First I sort by start time, then I create all possible subsets and take the longest possible value. This works. But I want to do this using Dynamic programming.

This problem screams DP, but I am not able to figure out if this has an optimal substructure.

My recurrence relation: `f(i, j) = f(i + 1, j) or f(i + nums[i], j) if nums[i].start > f[i].end`

Can someone help me figure out the thought behind the dp solution for the sub-problem?

Note: this problem is slightly different from job scheduling.

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## Do PCs earn an income besides what they earn while adventuring?

In Warhammer FRP 2nd edition your character is an adventurer (duh), yet they also have a career which they’ve been (and are still) supposedly pursuing, especially inbetween adventures.

You know, by day you’re a barber-surgeon pulling teeth and treating the sick, in the evening and during holidays you go and free your kidnapped aunt from the clutches of vile cultists who also happen to have some gold which you reappropriate for the betterment of society from their dead bodies. Next Monday you’re back at the barber shop curing dandruff and whatnot, for which services the citizens of the Empire pay you, as usual. Or maybe you’re a noble and you’re simply sent your due each Monday while you do whatever you feel like doing.

That you’re an active participant of your career path not just an ex-member is reinforced by the fact that you progress according to your career, and you most likely enter new basic/advanced careers as time passes in the campaign world. For example, the Basic Considerations of the core book (p.28) cautions that you can’t become the Steward of a castle and then leave for 6 months on an adventure, unless your GM says so. Which implies you should be getting paid if you manage to successfully take on the Steward career at a castle — especially if you don’t leave for 6 months (unless you do it at the request of the Lord of the castle.)

My question is:

Do WFRP 2nd edition PCs earn an income based on Table 5-1: Income (p.104) from their career besides what they earn (and loot) while adventuring?

Sure, I can decide this as a GM, but I’d like to know the official take or recommendation which I tried to yet couldn’t find in the core book. If it’s there, please, give me a page number.

## Is Crafting less lucrative than any other way to Earn Income?

One of my players in an upcoming game came up to me and noted that crafting items takes a ridiculously long time and/or is not much cheaper than just buying the item. This got me to look into the crafting system a bit deeper.

This is question #1, dealing with the money you save vs. buying on the market. Here is #2, about crafting times.

If you successfully craft an item, you get the same benefits as if you hold a job of your level. Instead of getting coinage, you lower the amount you have to pay for the item you create. But, to start crafting, you need to spend 4 days in which you gain no cost reduction, you always have to invest half of the list price. Also, you have to obtain a formula. In contrast, Earning Income the basic way, you get paid for every day you work.

Bottom line, by crafting you give up 4 days’ pay plus the cost of the formula.

I am aware of the following factors:

• You might not be able to find work of your level, while crafting always uses your level to determine profit.
• The item you want might not be up for sale. But, the formula might not be either.
• You can reuse the formula. The value of this will vary based on the item.

Is there any rule that I missed or misinterpreted? Or is Crafting really just a reflavoring of Earn Income, providing meager or circumstantial benefits?

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