https://www.freemathhelp.com/forum/threads/need-help-with-making-different-price-items-maintain-a-set-average

[TomOsiris]

Stuck, please help

I have 3 grades of product; High (h), Middle (m), Low (l), and Scrap (s)
The average (mean) price of these items must be $3.25/lb
Scrap price (s) must $0.50/lb. This is only set price, the rest are variable.

The price ratios I need to maintain are;
m=1.375*(l)
h=1.75*(l)

I need to solve for (l), which will give me prices for (m) and (h)

all of the above grades will have various amounts. for example,

(s)* 40,000 lb 0.4(t)
(l)* 30,000 lb 0.3(t)
(m)* 15,000 lb 0.15(t)
(h)* 15,000 lb 0.15(t)

In this example, we have 100,000 total lb. = (t)
The total price for these items is $325,000 $3.25(t)

since (s) = $0.50/lb, we can determine that we paid $305,000 for the rest of the three grades. $325,000 - (40,000*0.5) = $305,000
since we have twice as much (l) as the 2 other grades, we can simplify that to 2(l)+1.375(l)+1.75(l) = 305,000

This where I'm getting a bit lost. I need to know how to formulate an equation so that I can change any/all of the amounts per grade, and extrapolate the correct ratio prices for (l), (m), and (h); and the average (mean) price of (l),(m),(h), and (s) always is $3.25

Please send help, I can't figure it out

 

[Steven G]

(s+l+m+h)/4 = 3.25
That is (.5 + l + 1.375*(l) +1.75*(l) )/4 =3.25
(.5 + l + 1.375*(l) +1.75*(l) ) = 13
Can you solve for l from here?
Is this what you need?

 

[TomOsiris]

yes, but its not that simple, due to the different amounts per grade.
in this example I have 30,000 (l) compared to 15000 (m) and 15000 (h), so i understand that this needs to be a weighted average
I do not know how to formulate the equation to incorporate the relationships between the different amounts, and maintain the correct ratios between (l) (m) and (h)