Question

Prove that the EOQ cost function can be rewritten as

Answer 1

Answer:

the EOQ cost function $\mathbf{g(Q)= \dfrac{h}{2 \lambda Q}( Q- \sqrt{\dfrac{2 \lambda K }{2}})^2 + \sqrt{\dfrac{2 h K}{\lambda}}}$

Step-by-step explanation:

Given that:

$g(Q) = \dfrac{h}{2 \lambda Q} \begin {pmatrix} Q- \sqrt{\dfrac{2 K \lambda}{h}} \end {pmatrix}^2 + \sqrt{\dfrac{2 Kh}{\lambda}}$

Total cost = Purchase Cost + Ordering Cost + Holding Cost

i.e

T = $P \lambda + h \dfrac{Q}{2}+\dfrac{\lambda K}{Q}$

By differentiating with respect to Q and equating to zero, we have:

$0 = 0 +\dfrac{h}{2}- \dfrac{\lambda K}{Q^2}$

$Q* = \sqrt{\dfrac{2 k \lambda}{h}}$

Now;

$T = P \lambda + \dfrac{h}{2Q}(Q-Q^*)^2 + hQ^*$

$T = \dfrac{h}{2Q}(Q- \sqrt{\dfrac{2 \lambda K}{h}})^2 + \sqrt{2 hK \lambda } + P \lambda$

$(\dfrac{T - P \lambda}{\lambda }) = \dfrac{h}{2 \lambda Q}( Q- \sqrt{\dfrac{2 \lambda K }{2}})^2 + \sqrt{\dfrac{2 h K}{\lambda}}$

Therefore:

the EOQ cost function $\mathbf{g(Q)= \dfrac{h}{2 \lambda Q}( Q- \sqrt{\dfrac{2 \lambda K }{2}})^2 + \sqrt{\dfrac{2 h K}{\lambda}}}$