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Hi mathletes,

I'm usually OK with basic arithmetic, but I am having a serious mental block with whether an answer to my problem is even knowable, given the variables I have to work with.

I am essentially trying to update cost and price info on a large number of baked goods quickly and simultaneously, given a known change in the cost of a raw ingredient that's common to several confections.

Say flour costs me $1/lb. But it suddenly goes up 10% to $1.10/lb. Flour is in nearly every confection I sell, so I would like to make an equation (preferably in Excel) that would show my new cost/LB (from which I'd derive a selling price) for all my recipes. (In case anyone wonders, this isn't how I do business exactly, but for the sake of clarity, it's how I'm describing it.)

*Here's the info I have at my disposal:*

\-Ingredient Cost % Change (in this example, flour is up 10%)

\-The cost of all my completed recipes per LB. For example, my cost for chocolate chip cookie dough is $3.00/LB.

\-The percentage that the ingredient in question exists in the finished recipe. For example, flour exists at a rate of 50% per LB of finished cookie dough.

*Here's what I do not have:*

\-The full recipe (all ingredient line items and their respective percentages) for each finished good. I ONLY know the percentage by weight of the raw material (flour) in question for a list of recipes.


*I'm probably explaining this poorly, so I'll show you a full example:*

\-My vendor surprises me by letting me know flour will go up 10% the next time I buy it.

\-My current cost for flour is $1/LB. The new price will be $1.10/LB. So I know flour will increase by 10%.

\-Most of my confections call for flour in varying amounts. Flour may comprise 50%--by weight (not volume)--of a LB of choc chip cookie dough. Flour may comprise 2% by weight of something else, and 23% of yet another thing.

\-I can quickly get a computerized listing of all my recipes that contain flour and what percentage by weight it exists in the finished recipe. I cannot see any other ingredient percentages nor their costs.

\-I can quickly get a listing of the finished cost per pound of all of my recipes. Choc chip dough is $3/LB.

**Is there a way** to compute how much the **finished cost per pound** of **each** recipe goes up, knowing **only** the rate of increased cost of a single raw material and the **percentage it exists** in the recipe?


If you read this far, I hope I didn't cross too many eyeballs. Thanks in advance for any assistance!
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It appears that you do have enough information to calculate what you want, even without the final cost.

For example, say you have a recipe (chocolate chip cookies) that's initially 33% flour and flour is 1$/lb, that means you spend 0.33$/lb on flour per chocolate chip cookie (33% = 0.33, 1$/lb * 0.33 = 0.33$/lb)

Then all of a sudden, due to supply chain issues or something similar, the price of flour rises to 1.10$/lb, the same calculation can be applied with the new price (1.10$/lb * 0.33 = 0.36$/lb). This is the new cost of flour per pound of chocolate chip cookies produced.

Finally, to calculate the increase in price, you subtract the old price from the new one (0.36$/lb - 0.33$/lb = 0.03$/lb). This is how much your final price has increased.

In general, the formula for the price increase would be x = (N-n)*p, where x is the price increase, N is the new price, n is the original price, and p is the percentage of ingredient used in the recipe (expressed as a decimal).

and therefore the new price would be C = (c + x), where C is the new price, c is the original price, and x is the price increase.

Alternatively, you can combine the two formulas above to give C = c + (N-n)*p
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ok i thought about it a while and I think you should:

find out how much more your flour costs you (eg per month). Say +300$

then add how much your flour products earn you (per month). Say 3000$

then calculate how much you would need to increase their prices to make up for the increased cost.

here it is 300/3000 = 0.1 = 10%

now increase all prices of flour products by 10%. This is kind of a simple way to achieve roughly what yiu want.

Okay now you might want to distribute these 10% not evenly but according to how much flour is used by each recipe.

Say you bake 11 different recipes using all the flour of a month.

5% of the monthly flour is used by the first 5 recipes each. A few recipes use more flour (10%) and one recipe uses even more (25%) of the monthly flour.

1 - 5%   
2 - 5%   
3 - 5%   
4 - 5%    
5 - 5%   
6 - 10%    
7 - 10%   
8 - 10%    
9 - 10%    
10 - 10%    
11 - 25%   

now recipes 1 to 5 should cost more to account for 5% of the 300$. Which is 15$. So they each need a price increase which results in 15$ more earnings. (!! probably it does NOT need to increase earnings but "just" account for rhe 15$)

6 to 10 is 30$

11 is 75$

Now while thinking through this i found there are so many things you can include in the calculations.

Here are a few of them:

- item prices ideally should have a formula including salaries, rent, advertisement cost, basically everything, and of course the ingredients.

- do you want to cover your extra ingredient costs by increasing prices of the items using the ingredient (which is what the above is doing) OR

- just increase the price of items according to the ingredient prices (which is probably more what you wanted to do). Both things are very similar but still different.

Oh my god there are so many things to consider here. Its a fun problem but i do not have more time right now. Hope it helps a little.

Any additional infos, eg how you usually create the prices, would be helpful.

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