Conceptual Overview: Explore how to find the optimal order quantity for uniform demand.

A buyer for a store must decide six months in advance how many items of a seasonal product to purchase. Buying too few items will mean lost sales. Assume the lost profit from those sales Cu $=$ $$20$ per item. On the other hand, buying too many will result in lower profits from the items sold at a season$-$ending sale. Assume those costs Cs $=$ $$10$ per item. The optimal order size Q must satisfy this condition:

$$

$($

$$

$$

$$

$$

$$

$$

$<=$

$$

$$

$)$

$=$

$$

$$

$$

$$

$+$

$$

$$

$=$

$2$

$0$

$2$

$0$

$+$

$1$

$0$

$=$

$2$

$0$

$3$

$0$

$=$

$2$

$3$

$=$

$0$

$.$

$6$

$6$

$7$

P$($demand$<=$Q

$$

$)=$

C

u

$$

$+$C

s

$$

C

u

$$

$$

$=$

$20+10$

$20$

$$

$=$

$30$

$20$

$$

$=$

$3$

$2$

$$

$=0\mathrm{.}667$