Derive the annual average total cost

$$

$($

$$

$,$

$$

$)$

$$expression for a EOQ model with finite production rate

$$

$,$

$$constant demand rate

$$

$,$

$$shortage cost

$/$

backorder cost

$$

$$

$$per unit and holding cost

$$

$$per unit.

Also, derive that the minimum order quantity is

$$

$*$

$*$

$=$

$2$

$$

$$

$($

$$

$+$

$$

$$

$)$

$$

$$

$$

$($

$1$

$-$

$$

$$

$)$

$$and the minimum backorder

quantity is

$$

$=$

$$

$*$

$*$

$$

$($

$1$

$-$

$$

$$

$)$

$$

$+$

$$

$$

$$where

$$

$$is the fixed set up cost

$.$

$($

Hint: You need to take the partial

derivative of the average annual cost with respect to

$$

$$and

$$

$$and solve them to get the minimum

order quantity and the minimum back order quantity

$)$