Math Is Fun Forum

Eric

Guest

Help with maximization problem

Hi everyone, I need help figuring out how to do a problem like this so I can input the equation into Excel.  Sorry if this is a simple equation, but I've been out of college for a while now and I can't figure this out for the life of me!

Onto the question:

How do I find out how many of each product is being purchased based on these factors?

I have $500 total to spend

Product A cost $1.20
Product B cost $5
Product C cost $8

Product A must = 10% of total amount of products being purchased.
Product B must = 25% of total amount of products being purchased.
Product C must = 65% of total amount of products being purchased.

If I'm leaving some pertinent info out, just let me know what else you need.  Thanks for the help!

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Help with maximization problem

A+B+C = 100%, which is a good start!

Product A: 10% of $500 = $50, $50/$1.20 = 41.666... (ie 41 2/3)
Product B: 25% of $500 = $125, $125/$5 = 25
Product C: 65% of $500 = $325, $325/$8 = 40.625

Now, I imagine you can't buy a fraction of a Product, so a decision has to be made.

And by the sound of it, you are required to have the 10%/25%/65% breakdown, but you are allowed to spend less than $500, am I right? (if it was me, I would just buy 25 of B, 40 of C, and spend the rest on A, but that would not give the exact percentages)

So, if you want to play in Excel, then I would lay the formulas out like I did up top, and then reduce the $500 amount until it all works out.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: Help with maximization problem

maximization is killing everyone today!

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A logarithm is just a misspelled algorithm.

Eric

Guest

Re: Help with maximization problem

Thanks for the reply!  Unfortunately, I wasn't clear with what I was looking for.  Sorry about that!  Let me try and clear things up a bit...

When I said:
Product A must = 10% of total amount of products being purchased.

What I meant about product A equaling 10%, was not 10% of the money used for the purchase, but 10% of the total amount of goods being bought.  Hopefully this will make things a bit clearer:

Total amount of products being purchased = X (unknown)

Amount of product A being purchased must = 10% of X.
Amount of product B being purchased must = 25% of X.
Amount of product C being purchased must = 65% of X.

-------------------------------------------------------------

The complete question would be:

How do I find out how many of each product is being purchased based on these factors?

I have $500 total to spend

Product A cost $1.20
Product B cost $5
Product C cost $8

Total amount of products being purchased = X (unknown)

Amount of product A being purchased must = 10% of X.
Amount of product B being purchased must = 25% of X.
Amount of product C being purchased must = 65% of X.

Thanks again!!!

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Help with maximization problem

Ahh ... makes sense.

So, let us say you buy 10 "A"s, 25 "B"s and 65 "C"s, how much will that cost?

10×$1.20 + 25×$5 + 65×$8 = $12 + $125 + $520 = $657 ... whoops we blew the budget!

Let us scale our expectations back by 500/657 = 0.761

But 10×0.761 = 7.61 of "A" ... can you buy a fraction of a product? Does it matter if you don't get the percentages exactly right?

Anyway, you can play with it in Excel like this:

		  0.6		
A	10	6	   $1.20 	 $7.20 
B	25	15	  $5.00 	 $75.00 
C	65	39	 $8.00 	 $312.00 
		         	         $394.20

The "0.6" is used to multiply the 10, 25 and 65, then 6×$1.20=$7.20, well you get the idea

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Eric

Guest

Re: Help with maximization problem

Thanks a TON!  Life is now back in paradise