The economic order quantity with backlogging derived without derivatives

In previous work the EOQ formula without consideration to backlogging has been given a derivation without reference to the use of derivatives, neither for necessary conditions nor for second-order sufficient conditions. Furthermore, this algebraic derivation immediately provided the value of the average cost function in optimum. This paper extends the previous result to the EOQ formula taking the backlogging case into consideration. It is shown that a similar derivation immediately provides the corresponding results for this case.