Approaches on how to analyze product allocation (for multiple warehouses) by region in R?

Question

Consider the following dataset:

#   color  type region_west region_cent region_east region_west_pct region_cent_pct region_east_pct
# 1   red shirt          24          17          48          0.2697          0.1910          0.5393
# 2  blue shirt          24          18          44          0.2791          0.2093          0.5116
# 3   red  pant          42          13          33          0.4773          0.1477          0.3750
# 4  blue  pant          46          17          41          0.4423          0.1635          0.3942
# 5   red   hat          46          38           8          0.5000          0.4130          0.0870
# 6  blue   hat          40          11          21          0.5556          0.1528          0.2917

color and type should be self explanatory - we can say the region column represent "sales" and percent of sales by row.

What are some approaches for answering questions such as:

1. Is color and/or type statistically different by region? Which regions? (e.g. post-hoc testing)
2. How many (or what percent) color = red items should I put in the West?
3. How many (or what percent) type = pant items should I place in the East?
4. How would you express a confidence interval around the number of color = red items in the West? What about a confidence interval for the percentage?
5. How are you correcting for making multiple comparisons? (e.g. Bonferonni)

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Additional Assumptions: Assume these values represent a true population total sales. That is, all possible sales from the West, Central, and East region -- effectively demand. Additionally, we can assume the sales were made online and the customer resides in one of the three regions. This is essentially a warehouse distribution problem - say I have three warehouses, West, Central, and East - how much of each product should I place in each warehouse if these distributions are the assumed demand quantities.

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My initial thoughts are chi-square, ANOVA, and/or regression/glm/gam but I thought this is a "neat" little example hitting on a lot of fundamentals represented on this board, so I'm hoping to get some variety in the responses.

Here's the original dataset:

df <- structure(list(color = structure(c(1L, 2L, 1L, 2L, 1L, 2L), .Label = c("red", "blue"), class = "factor"), type = structure(c(1L, 1L, 2L, 2L, 3L, 3L), .Label = c("shirt", "pant", "hat"), class = "factor"),     region_west = c(24L, 24L, 42L, 46L, 46L, 40L), region_cent = c(17L,     18L, 13L, 17L, 38L, 11L), region_east = c(48L, 44L, 33L,     41L, 8L, 21L), region_west_pct = c(0.2697, 0.2791, 0.4773,     0.4423, 0.5, 0.5556), region_cent_pct = c(0.191, 0.2093,     0.1477, 0.1635, 0.413, 0.1528), region_east_pct = c(0.5393,     0.5116, 0.375, 0.3942, 0.087, 0.2917)), .Names = c("color", "type", "region_west", "region_cent", "region_east", "region_west_pct", "region_cent_pct", "region_east_pct"), out.attrs = structure(list(    dim = 2:3, dimnames = structure(list(Var1 = c("Var1=red",     "Var1=blue"), Var2 = c("Var2=shirt", "Var2=pant", "Var2=hat"    )), .Names = c("Var1", "Var2"))), .Names = c("dim", "dimnames")), row.names = c(NA, -6L), class = "data.frame")

Here's the dataset in a "tidy" format:

df.tidy <- structure(list(color = structure(c(1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L), .Label = c("red", "blue"), class = "factor"), type = structure(c(1L, 1L, 2L, 2L, 3L, 3L, 1L, 1L, 2L, 2L, 3L, 3L, 1L, 1L, 2L, 2L, 3L, 3L, 1L, 1L, 2L, 2L, 3L, 3L, 1L, 1L, 2L, 2L, 3L, 3L, 1L, 1L, 2L, 2L, 3L, 3L, 1L, 1L, 2L, 2L, 3L, 3L, 1L, 1L, 2L, 2L, 3L, 3L, 1L, 1L, 2L, 2L, 3L, 3L), .Label = c("shirt", "pant", "hat"), class = "factor"),     region = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,     2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L,     2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 1L, 1L, 1L,     1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L    ), .Label = c("region_west", "region_cent", "region_east"    ), class = "factor"), sales = c(24L, 24L, 42L, 46L, 46L,     40L, 17L, 18L, 13L, 17L, 38L, 11L, 48L, 44L, 33L, 41L, 8L,     21L, 24L, 24L, 42L, 46L, 46L, 40L, 17L, 18L, 13L, 17L, 38L,     11L, 48L, 44L, 33L, 41L, 8L, 21L, 24L, 24L, 42L, 46L, 46L,     40L, 17L, 18L, 13L, 17L, 38L, 11L, 48L, 44L, 33L, 41L, 8L,     21L), pct = c(0.2697, 0.2791, 0.4773, 0.4423, 0.5, 0.5556,     0.2697, 0.2791, 0.4773, 0.4423, 0.5, 0.5556, 0.2697, 0.2791,     0.4773, 0.4423, 0.5, 0.5556, 0.191, 0.2093, 0.1477, 0.1635,     0.413, 0.1528, 0.191, 0.2093, 0.1477, 0.1635, 0.413, 0.1528,     0.191, 0.2093, 0.1477, 0.1635, 0.413, 0.1528, 0.5393, 0.5116,     0.375, 0.3942, 0.087, 0.2917, 0.5393, 0.5116, 0.375, 0.3942,     0.087, 0.2917, 0.5393, 0.5116, 0.375, 0.3942, 0.087, 0.2917    )), row.names = c(NA, -54L), class = "data.frame", .Names = c("color", "type", "region", "sales", "pct"))

Feel free to expand the dataset to a larger example.