Answer:
20,000 pairs of barber scissors.
Step-by-step explanation:
The sales volume V for barber scissors is directly proportional to the size S of the sales force and inversely proportional to the price P of the scissors.
In other words, we can write that:
[tex]\displaystyle V = \frac{kS}{P}[/tex]
Where k is the constant of proportionality.
19,440 pairs were sold in 2013, when there was 54 salespeople and the price was $20 a pair. Hence, V = 19440 when S = 54 and P = 20. Substitute and determine the value of k:
[tex]\displaystyle \begin{aligned} (19440) &= \frac{k(54)}{(20)} \\ \\ 19440 &= \frac{27}{10}k \\ \\ k &=\frac{10}{27}(19440) = 7200 \end{aligned}[/tex]
Hence, our equation is:
[tex]\displaystyle V = \frac{7200S}{P}[/tex]
We want to determine the sales forecast with 50 salespeople and a price of $18 a pair. Hence, S = 50 and P = 18:
[tex]\displaystyle \begin{aligned} V&= \frac{7200(50)}{(18)} \\ \\ &= 20000\end{aligned}[/tex]
In conclusion, 20,000 pairs of barber scissors can be expected to be sold.
