Question

16. The purchase price of material Y is ? 400 per kg. The carrying cost of material in store comes or to be 10% of purchase price per annum and the ordering cost (fixed) per order is 2 400. If the sun total ordering cost and carrying cost of the year is 4,000, determine : (a) Economic order size (in kg) (b) Total Annual Demand of Material (in kg) (c) Annual Total Cost of Material Consumed. Ans.(a) 100 kg (b) 500 kg (c) * 2,04,000 P1​

Answer 1

Given:

The purchase price of material Y is 400 per kg. The carrying cost of material in the store comes or is to be 10% of the purchase price per annum and the ordering cost (fixed) per order is 2400. If the sun total ordering cost and carrying cost of the year is 4,000

To Find:

determine :

(a) Economic order size (in kg)

(b) Total Annual Demand of Material (in kg)

(c) Annual Total Cost of Material Consumed.

Solution:

It is given that the ordering cost is 400, carrying cost is 10% of purchase cost per kg which is 10%*400=40. It is given that the sum of total carrying cost and total ordering cost is 4000. Since the values of total carrying and ordering cost are equal then total carrying cost is 2000 and total ordering cost is 2000.

The formula for Total carrying cost(TCC) is,

$TCC=\frac{economic order quantity(q)*carrying cost(c)}{2}$

Now,

$2000=\frac{q*40}{2}\\q=100$

Now the formula for economic order quantity (q) is,

$q=\sqrt{\frac{2*annual demand(A)*ordering cost(O_{c})}{carrying cost(pu.pa)(C_{c})} }$

Now,

$100=\sqrt{\frac{2*A*400}{40} } \\10000=A*2*10\\A=500$

Annual requirement(A)=500 units

Quantity per order(B)=100

Number of orders(C)=A/B=5

Purchase cost per unit(D)=400

Cc(B/2*40)=2000

Oc(C*400)=2000

purchase cost(A*D)=200000

Total cost=240000

Hence, the Economic order size is 100kg, the Total annual demand of material is 500kg and the Annual total cost of material consumed is 240000.