Question

Consider the following:

$\text{Demand = 1000 units}$

$\text{Unit cost = Rs. 100}$

$\text{Order cost = Rs 160 per order}$

$\text{Inventory carrying cost = Rs. 20 per unit per year}$

$\text{back order cost = Rs. 10}$

Then what will be the selling cost per unit for no profit and no loss condition.

• A. Rs. 105
• B. Rs.102.5
• C. Rs.101.5
• D. Rs.100

Answer 1

The correct option is C Rs.101.5

$\text{EOQ,}$

$Q=\sqrt{\frac{2D{C}_0}{C_h}\left(\frac{C_b+C_h}{C_b}\right)}$

$=\sqrt{\frac{2\times 1000\times 160}{20}\left(\frac{10+20}{10}\right)}\text{= 219 units}$

$\text{Maximum inventory level,}$

$Q_m=Q\left(\frac{C_h}{C_b+C_h}\right)=219\left(\frac{10}{10+20}\right)\text{=73 units}$

$\text{Overall total cost = material cost + carrying cost}\text{+ ordering cost + shortage cost}$

$=C\times D+\frac{1}{2}\frac{Q_m^2}{Q}\times C_h+\frac{D}{Q}\times C_0+\frac{(Q-Q_m{)}^2}{2Q}\times C_b$

$=100\times 1000+\frac{1}{2}\times \frac{{73}^2}{219}\times 20+\frac{1000}{219}\times 160+\frac{(219-73{)}^2}{2\times 219}\times 10=101460.6$

$\text{For no profit, No loss,}$

$\text{Total sales = Total cost}$

$1000\times S.C=101460.6$

$\Rightarrow S.C=Rs.101.46$