Posts Tagged problem

Funny Provision problem

Posted by micdah in math on March 22, 2010

Recently I ran into a situation where I wanted to calculate a provision so that it was equal to a certain percentage of the total price but I only knew the production price. It quickly became obvious that is wasn’t as trivial as I had thought.

So stating the problem more clearly; We know the production cost c of some product and we want to determine a provision p_v so that it is equal to a percentage p_r of the sales price s.

We know that the sales price is the production cost plus the provision:
s = c + p_v

Our requirement can thus be stated as:

s(1 - p_r) = s - p_v
(c + p_v)(1 - p_r) = c
c(1 - p_r) + p_v(1 - p_r) = c
c(1 - p_r) - c = -p_v(1 - p_r)
\frac{c(1 - p_r) - c}{1 - p_r} = -p_v
p_v = -\frac{c(1 - p_r) - c}{1 - p_r}

Thus we can use this formula directly to calculate a provision matching a certain percentage of the sales price knowing the production cost and said percentage only.

As an example say you have a production cost of 242,- and want 15% of the sales price to go to provision, then we can calculate how much you should add in provision and by definition what your sales price should be:

c = 242, p_r = \frac{15}{100}
p_v = -\frac{242(1-\frac{15}{100})-242}{1-\frac{15}{100}} = \frac{726}{17} \approx 42.71
s = c + p_v \approx 284,71

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