Chapter 2.3, Problem 12E

Stock Turnover at Retail In retail sales, an important marker of retail activity is the stock turnover at retail. This figure is calculated for a specific period of time as the total net sales divided by the retail value of the average stock during that time, where both are measured in dollars. As a formula, this is written $\mathrm{S}\mathrm{t}\mathrm{o}\mathrm{c}\mathrm{k}\mathrm{ }\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{n}\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}=\frac{\mathrm{N}\mathrm{e}\mathrm{t}\mathrm{ }\mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{s}}{\mathrm{A}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{ }\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{c}\mathrm{k}\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{ }\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{a}\mathrm{i}\mathrm{l}}.$

This formula expresses stock turnover as a function of net sales and average stock at retail.

a. Suppose that your store had net sales of $682, 000 in men’s shoes over the past six months and that the retail value of the average stock of men’s shoes was $163, 000. What was the stock turnover at retail for that time period?

b. Suppose that in a certain month, your store’s net sales of women’s dresses were $83, 000 and that the usual stock turnover at retail is 0.8 per month. What do you estimate to be your store’s average stock at retail?

c. Solve the equation for average stock at retail- that is, write a formula giving average stock at retail as a function of stock turnover and net sales.

d. Suppose that in a certain time period, your store had an average stock of socks with a retail value of $45, 000 and a stock turnover at retail of 1.6. What were the store’s net sales of socks during that time period?

e. Solve the equation for net sales- that is, write a formula giving net sales as a function of stock turnover and average stock at retail.