Question

A manufacturing company XYZ purchases 50000 parts of a machine for its annual requirements; each part costs ₹40. The ordering cost per order is ₹25 and the inventory holding charges are 10% of the unit cost per year. If the maximum quantity that can be ordered at a time is 600. What will be the minimum total inventory cost?

• A. ₹ 3383.3
• B. ₹3162.3
• C. ₹ 3283.3
• D. ₹ 3362.3

Answer 1

The correct option is C ₹ 3283.3

$D=50000$

$C_0=25,C_u=40,C_h=0.1of{C}_u=0.1\times 40=4$

$EOQ=\sqrt{\frac{2D{C}_0}{C_h}}=\sqrt{\frac{2\times 50000\times 25}{4}}=790.569units$

$\because EOQ>\text{Maximum quantity ordered at once.}$

$(TIC{)}_{Q=600}=\frac{D}{Q}\times C_o\times \frac{Q}{C}\times C_h=\frac{50000}{600}\times 25+\frac{600}{2}\times (40\times 0.1)$

$=3283.33$

$\text{Alternate:}$

$TIC=\frac{\sqrt{2D{C}_0{C}_h}}{2}[k+\frac{1}{k}]\{k=\frac{Q^{\ast }}{Q}\}$

$=\frac{\sqrt{2\times 50000\times 25\times 4}}{2}[1.317615+0.758947]$

$TIC=₹3283.33$