Question

Annual demand for window frames is 10000. Each frame costs Rs. 200 and ordering cost is Rs. 300 per order. Inventory holding cost is Rs. 40 per frame per year. The supplier is willing to offer 2% discount if the order quantity is 1000 or more, and 4% if order quantity is 2000 or more. If the total cost is to be minimized, the retailer should

1. order 200 frames every time
2. accept 2% discount
3. accept 4% discount
4. order Economic Order Quantity

Answer 1

Correct Answer - Option 3 : accept 4% discount

Concept:

For dscount model at different price break, find total cost at each price break and EOQ.

Calculation:

Given:

D = 10000 units; C_u = Rs. 200

C_o = Rs. 300/order ; C_h = 40 per frame/year.

EOQ = \(\sqrt {\frac{{2D{C_o}}}{{{C_h}}}} \)= 387.298

\(Total \ cost,TC=DC+\frac {Q}{2}C_h +\frac {D}{Q}C_o\)

At EOQ,

\(TC=(10000)(200)+\frac {387.298}{2}(40) +\frac {10000}{387.298}(300)=Rs. 2015492\)

At Q = 1000, discount of 2%:

\(TC=(10000)(200)(0.98)+\frac {1000}{2}(40) +\frac {10000}{1000}(300)=Rs. 1983000\)

At Q = 2000, discount of 4%

\(TC=(10000)(200)(0.96)+\frac {2000}{2}(40) +\frac {10000}{2000}(300)=Rs. 1961500\)

So, the minimum total cost is with a discount of 4%. Hence, select the 4% discount.