Warwick’s Workings, part II

This post will mainly make sense to Warwick – if you aren’t Warwick and you need some context, see the Twitter thread starting with this twitter post.

u_{cost} \text{ is the number of units at cost price}
p_{cost} \text{ is the unit cost price}
u_{current} \text{ is the number of units at the current price}
p_{current} \text{ is the current unit price}
p_{target} \text{ is the target unit price}

\frac {u_{cost} p_{cost} + u_{current} p_{current}} {u_{cost} + u_{current}} = p_{target}
\Rightarrow u_{cost} p_{cost} + u_{current} p_{current} = p_{target} (u_{cost} + u_{current})
\Rightarrow u_{cost} p_{cost} + u_{current} p_{current} = p_{target} u_{cost} + u_{current} p_{target}
\Rightarrow u_{current} p_{current} - u_{current} p_{target} = p_{target} u_{cost} - u_{cost} p_{cost}
\Rightarrow u_{current} (p_{current} - p_{target}) = u_{cost} (p_{target} - p_{cost})

\text{The formula you're after is:}
u_{current} = \frac {u_{cost} (p_{target} - p_{cost})} {(p_{current} - p_{target})}

\text{Proving it works using the given figures:}
u_{current} = \frac {336 * (14 - 18.23)} {(13 - 14)}
\Rightarrow u_{current} = \frac {(-1421.28)} {(-1)}
\Rightarrow u_{current} = 1421.28

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