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 a 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

• A. order 200 frames every time
• B. accept 4% discount
• C. accept 2% discount
• D. order Economic order Quantity

Answer 1

The correct option is B accept 4% discount

Total cost = Purchase cost + holding cost + ordering cost

It is a case of inventory with price breaks.

$EOQ,Q^{\ast }=\sqrt{\frac{2C_{n}D}{C_h}}=\sqrt{\frac{2\times 300\times 10000}{40}}$

$\text{= 387.298 units = 388 units}$

$\text{For EOQ Q* = 388 units}$

$T\left(C\right)=D\times C+\frac{Q^{\ast }}{2}\times h+\frac{D}{Q^{\ast }}\times A$

$=10000\times 200+\frac{388}{2}\times 40+\frac{10000}{388}\times 300$

$=2015491.959=Rs.2015492$

$\text{For Q = 1000}$

$\text{T(C) = 10000 × (200 × 0.98) + 500 × 40 + 10 × 300}$

$=Rs.1983000$

$\text{For Q = 2000}$

$\text{T(C) = 10000 × (200 × 0.96) + 1000 × 40 + 5 × 300}$

$=Rs.1961500$

$\text{Accept 4\% discount as lowest total cost at}$

$Q=2000$