Given a Hearthstone card collection how to determine the optimal card pack to purchase?

Hearthstone allows players to buy card packs with real money or in game currency. Each Hearthstone card pack has five cards with at least one card being rare or better. There have been several player card pack sampling studies done to determine the typical rarity makeup of a Hearthstone card pack:

                                        Common      Rare        Epic        Legendary
Percentage of total                     71.65%      22.84%      4.42%       1.10%
Count per 27,868 packs                  99,836      31,821      6,152       1,531
Probability of at least 1 per pack      99.81%      72.64%      20.21%      5.37%

Players can disenchant cards to create Arcane Dust which can then be used to create cards. The crafting and disenchanting costs for a card are determined by its rarity and foil (regular/golden):

Rarity                  Crafting Cost       Disenchanting Value
Common                  40                  5
Rare                    100                 20
Epic                    400                 100
Legendary               1600                400
Golden Common           400                 50
Golden Rare             800                 100
Golden Epic             1600                400
Golden Legendary        3200                1600

Given the above crafting and disenchanting costs and card pack composition statistics the expected dust value of a card pack is 97.8.

For the scope of this question having a complete playable set means ignoring the card's foil having one copy of every Legendary card and two copies of any of the following rarities: Common, Rare, and Epic for each card. A playable set assumes duplicative higher dust value cards will be disenchanted over low value equivalent cards.

It's easy to determine the dust needed to complete a collection, it's more difficult to determine which pack a player should buy. Given the probabilities of opening a pack with differing rarities and the expected dust value of a pack I want to determine which pack a player should buy.

Specifically, what I am looking for is a formula that can be used to determine the best card pack for a player to buy given their existing collection and desire to have a complete playable collection. Obviously as packs are opened the makeup of the player's collection changes and the next optimal pack to purchase may not be the same as the last.

I have been playing Hearthstone since it was in beta and have amassed a solid collection, but am still missing cards from all three of the current sets:

• Classic: 705/723 (302 collectible cards)
  • Common 336/336
  • Rare 162/162
  • Epic 66/74
  • Legendary 23/33
• GvG: 178/226 (123 collectible cards)
  • Common 80/80
  • Rare 70/74
  • Epic 22/52
  • Legendary 6/20
• TGT: 200/244 (132 collectible cards)
  • Common 97/98
  • Rare 69/72
  • Epic 28/54
  • Legendary 6/20

Using my collection as an example what would a formula look like to determine the optimal pack to purchase to create a complete playable collection?