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UESTION #4 A. Patrick & Terri Ltd. is a stationery store that buys stationery wh

ID: 326838 • Letter: U

Question

UESTION #4 A. Patrick & Terri Ltd. is a stationery store that buys stationery wholesale and then sells them retail, to the general public. In order to ensure that he has goods for sale, the manager has to order 1200 cases per year at a price of $100.00 each, as this is the amount demanded per year by customers. Management has calculated its insurance cost at $20.00 per order, interest cost at $15.00 per order and the cost of security $10.00 per order. Warehouse cost is $25.00 per year. The supplier offers a 6% discount for purchasing 50-99 cases and 8% for purchases of 100 or more cases at one time. What is the most economical amount to order at a time and why? (Show all working) 15 marks B. Why should the management of a firm spend so much time, money and effort managing its inventory? 5 marks

Explanation / Answer

Purchase price per unit, p     varies for different quantities of orders

Regular Purchase price per unit, p=   $100

Ordering cost, O= 20+15+10= $45 per order

Carrying cost per year per unit, C = $ 25

Annual Demand, d =      1200

First, let us find the optimal quantity (does not depend upon price)

Optimal order quantity, E.O.Q  

= SQRT(2 × Annual demand × Cost Per Order / Carrying Cost per unit per year)

= SQRT(2*1200*(45/25))

=65.73

EOQ=66 UNITS

When discounts are offered, the optimum order quantity is

Here the first minimum quantity eligible for a discount is 50 cases. But EOQ is above that. Hence we ignore this order quantity.

We move to the next discount option starting from 100 cases per order. So, now we have to compare the total costs at EOQ with total costs at other order quantities eligible for discount

Step 1

For order quantity, Q =66 &       Regular Purchase price, p= $100

Total annual cost= Purchase cost+ Inventory cost

= purchase cost+ ordering cost+ carrying cost

= p*d+   O* d/Q +   c * Q/2

= 100*1200 +    45 *( 1200/66)    +      25* (66/2)

= $ 121643.2

Step 2

For getting discount,

Order quantity =100 (we use the minimum order quantity eligible for discount)

Regular Purchase price, p=   100-8 (8 % discount) =$92

Total annual cost

= Purchase cost+ Inventory cost

= purchase cost+ ordering cost+ carrying cost

= p*d+   O* d/Q +   c * Q/2

= 92*1200 +    45 *( 1200/100)    +      25* (100/2)

= $ 112190

The total annual cost at discounted price is lower than when we buy at regular EOQ. Hence we buy at order quantity of 100 per order.

B.

Management puts so much effort in inventory management in order to