The Interstate Carpet Discount Store has annual demand of 10

The Interstate Carpet Discount Store has annual demand of 10,000 yards of Super Shag carpet. The annual carrying cost for a yard of this carpet is $1.25, and the ordering cost is $300. The carpet manufacturer normally charges the store $8 per yard for the carpet. However, the manufacturer has offered a discount price of $6.50 per yard if the store will order 5000 yards. How much should the store order, and what will be the total annual inventory cost for that order quantity?

Solution

Supposing that the carpet store makes N orders per year, Then the number of of carpets ordered will be 10000/N yards.

We assume that inventory is fully used up used in each order period.

This virtually means that the average stock or inventory with the store in order period is 1/2 of the order quantity, which is equal to 5000/N yards.

total annual cost (C) of ordering and warehousing at $8 per yard the carpet will then be

C=10000*8+150N+5000/N*0.75

C=80000+150N+375/N

Find the exact value of N by setting the first order derivative of Equation above equal to zero

150-3750/N²=0

N= 5, because n cannot be negative

The inventory cost at N = 5 orders per year is equal to I = (5000/5)*0.75=$750

Now that the carpet cost is 6.5, at N=2 (calculated using equation 1 of cost again with 6.5 as cost) the inventory cost will also change I = (5000/2)*0.75 =$1875

Now the cost for 10000 orders at $8 per yard and 5 orders per year

C=(10000*8+150*N+5000/N*0.75)

=80000+150N+375/N =$81500

Now the cost for 10000 orders at $6.5 per yard and 2 orders per year

C=(10000*6.5+150*N+5000/N*0.75)

=65000+150N+375/N =$67175