Chapter 14.2, Problem 47E

Wilson's lot size formula In economics, the most economical quantity Q of goods (TVs, dresses, gallons of paint, etc.) for a store to order is given by Wilsons lot size formula

$Q=\sqrt{2KM/h}$ where K is the cost of placing the order, M is the number of items sold per week, and h is the weekly holding costs for each item (the cost of storage space, utilities, taxes, security, etc.).

(a) Explain why $\frac{\partial Q}{\partial M}$ will be positive.

(b) Explain why $\frac{\partial Q}{\partial M}$ will be negative.