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I have been struggling with this question for a long time, Is there somebody kind enough to help?

If I received 1 free unit for 3 units purchased, how many units should I sell to issue 1 free unit? The purchase price and the selling price are the same. The expected profit is 10%.

Is there a formula?

Thanks & Regards, Girish

user131268
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1 Answers1

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Answer:

Revenue = $$[n_s - \frac{n_{s}}{k}].S$$

where $n_s$ => No of units ready for sale. $\frac{n_{s}}{k}$ is the free unit to be given away

Cost = $$n_{p}.P$$

We know now that $$n_s = n_p + \frac{n_{p}}{3}$$

$$\frac{[n_s - \frac{n_{s}}{k}] - n_p}{n_p} = .1$$ $$[n_s - \frac{n_{s}}{k}] = 1.1n_p$$ $$n_s.[1-\frac{1}{k}] = 1.1n_p$$

$$n_p.[1+\frac{1}{3}].[1-\frac{1}{k}] = 1.1n_p$$

$$[1-\frac{1}{k}] = \frac{3.3}{4}$$

$$\frac{1}{k} = .175$$

Now for one unit to be given free, it means that

$$\frac{n_s}{k} = 1$$

$$n_s = 5.71 = 6$$ Units to be sold

To use a little basic modular arithmetic ($n_s=40$) and you give away $7$ units and

$n_p =30$ resulting in a profit of $10 percent$. So for every $3$ units purchased you get an additional unit making it $40$ that are now available for sale and to make a profit of $10 percent$ you can choose to give away $7$ units.

Thanks

Satish

Satish Ramanathan
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