# WidgetFilterFebruary 22, 2011 1:53 PM   Subscribe

If I know the number of widgets, number of days, and total budget, can I break down a per widget price?

Say my factory makes 3 types of widgets. Also say my factory was open for 30 days, and produced the following:

Widget A: 80 widgets, 21 days of production
Widget B: 50 widgets, 23 days of production
Widget C: 70 widgets, 12 days of production

Widgets are created on separate machines, and can all be produced concurrently.

I know that the total expenses for the factory is \$1,000,000.

My question: can I get to an average price per widget by type?
posted by pencroft to Grab Bag (10 answers total)

posted by Pickman's Next Top Model at 1:54 PM on February 22, 2011

You could get to an "average" price - i.e., a price that treats each widget as the product of a certain number of machine-hours, and, assuming each machine-hour costs the same, price each widget such that the price is stable across all widgets and production times. But that "assuming" in the previous sentence is a pretty big assumption.
posted by Pickman's Next Top Model at 1:57 PM on February 22, 2011

You are short a number of necessary facts. To understand this type of analysis, go here:

http://www.cliffsnotes.com/study_guide/Cost-Volume-Profit-Analysis.topicArticleId-21248,articleId-21229.html

It is a short course in exactly what you are trying to do.
posted by Old Geezer at 2:05 PM on February 22, 2011

Assuming that 1 day of production is 8 man-hours (one shift, one laborer per shift), and labor is the primary cost (two big ifs), then the cost of one widget would be the ratio of that widgets man-hours to the total man-hours, or

A: 21/56*\$1M = \$375,000; divided by 80 widgets, call it \$4,700 per widget A
B: 23/56*\$1M= \$410,714; divided by 50 widgets, about \$8,200 per widget B
C: 12/56*\$1M = \$214,285; divided by 70 widgets about \$3,000 per widget C

I wouldn't trust these numbers for anything other than order-of-magnitude.
posted by muddgirl at 2:05 PM on February 22, 2011

not the cost of one widget - the cost of producing one type of widget... but I agree that this is a very rough approximation
posted by muddgirl at 2:06 PM on February 22, 2011

You could derive the share of the cost that each widget represents and then guess at a unit price if we assume that the percentages of widgets created is equal to their value as a share of the total cost.

Widget A = 80 * 21 = 1680 widgets
Widget B = 50 * 23 = 1150 widgets
Widget C = 70 * 12 = 840 widgets

Of the 3,670 widgets produced, 46% of them were Widget A.

Ergo, Widget A = \$460,000 = 273.80 per Widget A.

But there's some serious hand-waving here. We're assuming that 46% of the units = 46% of the value. That's not logical at all. Widget A could be worth pennies, while Widget C are worth far more.
posted by Cool Papa Bell at 2:14 PM on February 22, 2011

Do all machines require the same number of people to run them? Are all days of production the same length? Does this include setup and downtime? Do all machines use the same amount of overhead? Are all widgets made out of the same amount of raw material, or at least the same total cost of raw material? (To me, this is the most likely to be a no, and to have a major, material effect on the answer.)
posted by jeather at 2:15 PM on February 22, 2011

Do all machines require the same number of people to run them? Are all days of production the same length? Does this include setup and downtime? Do all machines use the same amount of overhead? Are all widgets made out of the same amount of raw material, or at least the same total cost of raw material? (To me, this is the most likely to be a no, and to have a major, material effect on the answer.)

Yes to all of these. Widgets all have the same raw material cost, but do not take the same amount of time to produce.
posted by pencroft at 3:24 PM on February 22, 2011

Does 80 widgets, 21 days of production mean that it took 21 days to make 80 widgets, or that you made 80 widgets/day for 21 days?
posted by jon1270 at 3:47 PM on February 22, 2011

If all machines take the same amount of overhead (electricity, square footage, etc) per hour-in-use, the same number of people to run them, and need the same setup time and the same number of people to do setup and have the same rate of downtime and need the same number of people to fix it, have the same amount of waste, and all widgets use the same amount (weight/volume) of the same kind of raw material, then yes, you can take the total costs, allocate 21/(21+23+12) of the cost to all of widget A and so on, then divide those costs by number of widgets made -- but in the real world, the machines will not be identical except for the amount of time it takes to make a widget.
posted by jeather at 5:12 PM on February 22, 2011

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