Chapter 1.5, Problem 83E

Lot Size The theory of economic lot size shows that, under certain conditions, the number of units to order to minimize total cost is

$x=\sqrt{\frac{kM}{f}}$,

where $k$ is the cost to store one unit for one year, $f$ is the (constant) set up cost to manufacture the product, and $M$ is the total number of units produced annually. Find $x$ for the following values of $f$, $k$, and $M$.

(a) $k=\$1$, $f=\$500$, $M=\mathrm{100,000}$

(b) $k=\$3$, $f=\$7$, $M=\mathrm{16,700}$

(c) $k=\$1$, $f=\$5$, $M=\mathrm{16,800}$