How to change to same units

Question

Could anyone help me change it into same units/ values? I need to have them all in "years"

Demand(D): Every month there is 5000 food: Therefore,

$D= 5000 * 12 = 60000$ food per year

Production(P): The foods can be produced up to 90000 per year: Therefore,

$P = 90000$ food per year

Holding cost(H): The foods are stored in bundles of 500, and each bundle has a holding cost of 30 dollars per month: Therefore, what I need is the holding cost for "1 food per year".

e.g. ??? dollars per food per year

I have tried something like this:

30/500 = 0.06 dollars per food per month. So if I do

0.06 * 12 = 0.74 dollars per food per year. (is this how I should write it?)

I dont understand the "bundle part". How can I convert it?

Any helps much appreciated!

Answer 1

What you have done is sensible, but may slightly understate the holding cost because of the issue of part of a bundle.

For example if you stored $3200$ food for a month, you might try $3200 \times \$0.06 = \$192$ as the monthly holding cost, but in fact you have $6.4$ bundles which might be charged the same as $7$ bundles, i.e. $\$210$ for the month.

So you may need to round up holding costs to a multiple of $\$30$ a month, which if the amount of food held does not change would involve rounding up to a multiple of $\$360$ each year.

Answer 2

Yes, you did it right.

In this context, a "bundle" is to a "food" as a "half-kilometer" is to a "meter". It's nothing more than a new unit to represent a larger amount of something, and we change between the two units by applying the conversion factor.

So a holding cost $H$ of 30 dollars per month for each bundle (i.e. per bundle) is the same as $$H=\frac{ 30\frac{\text{dollars}}{\text{month}}}{\text{bundle}}=\frac{ 30\frac{\text{dollars}}{\text{month}}}{\text{bundle}}\cdot\frac{1\text{ bundle}}{500\text{ food}} = \frac{3}{50}\frac{\frac{\text{dollars}}{\text{month}}}{\text{food}}.$$