Derive the annual average total cost G$($Q$,$s$)$ expression for a EOQ model with finite production rate P$,$ constant demand rate lambda, shortage cost$/$backorder cost Cs per unit cost h per unit. Also, derive that the minimum order quantity is Q$*=$ sqrt$((2$K$($Lambda$)($h$+$Cs$))/($hCs$(1-$lambda$/$P$)))$ and the minimum backorder quantity is s$=($Q$*$h$(1-$lambda$/$P$))/($h$+$Cs$)$ where k is the fixed set up cost$.($Hint: You need to take the partial derivative of the average annual cost with respect to Q

and s

and solve them to get the minimum order quantity and the minimum back order quantity$)$