\[D=k\left (1+\frac{M}{100} \right)[B+\lambda(I_Y-I_M)]\]

\[D=\left [\frac{k(B- \lambda I_M)}{100} \right ]M+\frac{\lambda kMI_Y}{100} +k \lambda I_Y+k(B- \lambda I_M) \]

\[\frac{dD}{dM}=\frac{k(B- \lambda I_M)}{100}+\frac{\lambda kI_Y}{100} \]

\[\frac{dD}{dM}=\frac{k[B+ \lambda (I_Y-I_M)]}{100} \]

\[\frac{dD}{dI_Y}=\frac{\lambda kM}{100}+\lambda k\]

\[\frac{dD}{dI_Y}=\frac{\lambda k(M+100)}{100}\]

\[\frac{dI_Y}{dI_M}=\frac{\triangle I_Y}{\triangle M} \]

\[\triangle I_Y=\frac{dI_Y}{dM} \]

\[\frac{dI_Y}{dM}=\frac{dI_Y}{dD}\frac{dD}{dM} \]

\[\frac{dI_Y}{dM}=\frac{100}{\lambda k(M+100)}\frac{k[B+\lambda (I_Y-I_M)]}{100}=\triangle I_Y \]

\[\triangle I_Y=\frac{\frac{B}{\lambda}+I_Y-I_M}{M+100} \]

\[\triangle I_Y=\frac{\frac{B}{\lambda}+I_Y-I_M}{M+100}=\frac{\frac{541}{2}+125-89}{71+100}=1.792 \]

\[\frac{1.02}{1.01}=1.00990=0.99% \]

\[\frac{1.51}{1.5}=1.00666=0.67% \]

Money, where art thou?

As detailed over at a recent post on the Bloggaru, I've found myself to be in a rather tight spot in terms of money. Thanks to me picking up RNG (of all jobs) on impulse, I quickly burned through a lot of my cash supply, and even with Celestria paying me a commission for each elemental bead carved up for her, I found myself with just 200k to my name.

Not exactly the best way to go for a Goldsmither, eh?

And so I sat down and scoured the lists for something to make. At Goldsmithing 86, that plus my Shades, Apron and Advanced Imagery brings me up to a virtual skill of 91. Hitting the 51-tier means targetting anything with a skill cap of 40 and below.

A few days ago, another fellow Goldsmithing, Nynaeve, mentioned that she was making nice money off synthesizing the Silver Ring +1 recipies. With that in mind, I quickly checked the AH, and set about to try and make me some Courage Rings +1.

Three stacks of Silver Ingots set me back another 90k. I picked up some Sardonyxes from the Lower Jeuno jewelry shop, and from the AH, averaging around 1.5k each, and of course picked up the requisite crystals, too.

I managed to turn three stacks of Silver Ingots into nine Silver Rings +1. The next step would be to turn all those into Courage Rings +1, the end result being that I got 4 Courage Rings +1 out of the whole deal. All in all, it took me a little over an hour to assemble, and with Courage Rings +1 selling for 50k on the AH, I make myself about 100k profit.

Not quite the numbers I was looking to put out, but for a 51-tier synth, I wasn't really expecting too much.

Nearing the end...

Starting Goldsmithing skill: 85.1
Skillup synth: Elemental Beads (various- cap 87)
Imagery Support: Advanced Imagery
Equipment of note: Auster's Staff, Goldsmithing Apron, Shaded Spectacles
Direction: South-East
Location: Bastok Goldsmithing Guild
Moghancement: Powerful Wind
Moon phase: Lightsday, Full Moon (100%)

85.1(+5)
9:38 Success, +0.1!

85.2(+5)
9:51 Success, +0.1!

85.3(+5)
10:04 Success.
10:17 Success.
10:31 Success, +0.1!

85.4(+5)
10:47 Success, +0.1!

85.5(+5)
11:00 Success, +0.1!

85.6(+5)
11:36 Success, +0.1!

85.7(+5)
11:49 Success.
12:01 Success.
12:13 Success.
12:25 Success.
12:38 Success, +0.1!

85.8(+5)
12:50 Success, +0.1!

85.9(+5)
13:08 Success.
13:37 Success.
13:51 Success.
14:04 Success.
14:18 Success.
14:31 Success, +0.1!



One last level of Elemental Beads to go. ^^

86.0
14:45 Success.
14:59 Success.
15:23 Success, +0.1!

86.1
15:35 Success.

I can see why they say Elemental Beads give good skillup. Actually, it seems to be the case that, although I occasionally got subpar skillup rates, a lot of my skilling sessions have at least averaged a +0.3 gain per twelve synths, but the number of these "streak" skillups off Beads is really quite remarkable, considering that I'm technically synthing over cap.

Anyway, Celestria and I met up again a few days later to continue:

Starting Goldsmithing skill: 86.1
Skillup synth: Elemental Beads (various- cap 87)
Imagery Support: Advanced Imagery
Equipment of note: Auster's Staff, Goldsmithing Apron, Shaded Spectacles
Direction: South-East
Location: Al Zahbi Goldsmithing Guild
Moghancement: Powerful Wind
Moon phase: Darksday, Waxing Gibbous (74%)

86.1
1:30 Success.
1:42 Success.
1:54 Success.
2:06 Success.
2:17 Success, +0.1!

86.2
2:31 Success.
3:00 Success.
3:12 Success, +0.1!

86.3
3:25 Success.
3:38 Success.
3:52 Success, +0.1!

86.4
4:05 Success.

At this rate, two more skillup sessions should bring me to cap. Then, goodness knows what...