Calculating a "fixed profit" on inventory

[1plus1is10]

Summary: Calculating a "fixed profit" on inventory

[Mentor Note -- after an initial move to the schoolwork forums, this thread turns out to be a General Math question after all (see posts #5-6), so it is moved back to the General Math forum]

I have 1000 products for sell in a store.
Some make money, and some lose money.
I want to maximize my overall profits by having a "fixed profit" on every product.

Meaning, price = cost + fixedprofitX, or:
p1=c1+X, p2=c2+X, p3=c3+X, p4=c4+X... p1000=c1000+X

How can I calculate X using only each product's average monthly profit?

Meaning, just using average1, average2, or:
a1, a2, a3, a4... a1000

My first thought is that X would be the square root of the sum of squares.
But the fact that some products lose money makes me think that is wrong.

Thanks for any help.

 

[berkeman]

I have 1000 products for sell in a store.
Some make money, and some lose money.
I want to maximize my overall profits by having a "fixed profit" on every product.

There are other variables in play in such a situation, no? Like sale volume changes with the price charged on each item. Price goes up and volume goes down, and there is an optimum price point for each based on that function for each item.

Without including that variable, it will be hard to solve this problem realistically. Anyway, I would start with a sample spreadsheet of about 10 example items and put in some numbers for current volume, cost, price and profit, and see if you can see a way to change the price of each to get you to the target constant profit (assuming no price-volume relationship as a simplification to start).

Also, why would earning a fixed profit on each product necessarily maximize your overall profit?

 

[FactChecker]

There is definitely something missing in the problem as you have described it. If there is no limit on how much you can charge, there is no maximum profit. Just take the cost of each product and add $X million to get the price.

 

[mfb]

If every individual object creates X profit and you sell k objects per month your profit is k*X. To increase that just increase X! Of course it doesn't work that way, your price will influence how much you sell. Every item will have its individual ideal selling point where you maximize the product of sales and profit per item for this specific item.

Requesting a fixed profit for every item is not a good strategy. Selling a $1000 item should come with more (absolute) profit than selling a $5 item. You might even sell that $5 item at a loss if it makes people much more likely to buy the $1000 item.

 

[1plus1is10]

Oh well.
It is obvious that my choice of using "products and sales" is a distraction to the math calculations I wish to learn about.

Allow me to use a different analogy...

A person shoots a cannon 1000 times at different angles.
Each cannonball has a different peak altitude.
Some are duds and fall out the end of the barrel with no altitude at all.

How can I calculate the highest average altitude?
...even better - of the biggest cluster (minimizing outliers)?

Meaning, highest altitude1, altitude2, etc. or:
a1, a2, a3, a4... a1000

What I want to know is similar in concept to what berkeman said "Price goes up and volume goes down".
Well, if I have a "fixed" peak too high then less cannonballs will hit that peak.
And the opposite is true, if I have a "fixed" peak too low then I'm missing out on the extra distance.

I am currently using brute-force (a.k.a. the Iterative Method).

I hope this helps.
Thanks.

 

[1plus1is10]

So, after searching the web even more, I now think the math question that I am asking is:

How do I calculate the Mode of a Skewed Distribution?

Maybe someone would be willing to tell me in layman's terms what this webpage says:
Mode of Grouped Data

I'm unfortunately a 1+1=2 level guy.

 

[1plus1is10]

Okay, forget that webpage reference now.
My problem is that my data (a1, a2, a3, etc.) are not convenient whole numbers that magically create a Mode.

 

[1plus1is10]

So, I discovered that I need to convert my data into a Histogram:
Wikipedia: Histogram

Then that will give me the Mode.
And, hopefully, that is what I need.

Coincidentally, I ran across the Central Limit Theorem:
Wikipedia: Central Limit Theorem

It makes me wonder if all I really needed was the Mean all along.
I guess I will find out.

 

[berkeman]

Okay, I guess this version of your thread was doomed from the start, so I'll close it now.

After you have done more work and research, go ahead and start a new thread if appropriate, and describe the exact problem you are trying to solve, and what part of the reading you have been doing confuses you (include the appropriate links). We are happy to help, but continuous movement of the goal will vex any good kicker.