Question

The I-75 Carpet Discount Store has an annual demand of 10,000 yards of super shag carpet. The annual carrying cost for a yard of carpet is $0.75 and the ordering cost is $150. 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 5,000 yards. How much should the store order, and what will be the total inventory cost for that order quantity?

Answer 1

5 units and $2,175

Step-by-step explanation:

a. The computation of the economic order quantity is shown below:

=
`\sqrt{\frac{2* \text{Annual demand}* \text{Ordering cost}}{\text{Carrying cost}}`

=
`\sqrt{\frac{2* \text{10,000}* \text{\$150}}{\text{\$0.75}}`

= 2,000 units

The total cost of ordering cost and carrying cost equals to

= Annual ordering cost + Annual carrying cost

= Purchase cost + Annual demand ÷ Economic order quantity × ordering cost per order + Economic order quantity ÷ 2 × carrying cost per unit

= 10,000 × $8 + 10,000 ÷ 2,000 × $150 + 2,000 ÷ 2 × $0.75

= 80,000 + $750 + $750

= $81,500

Now in case of ordering 5,000 yields at discount price of $6.50 the total cost is

= Purchase cost + Annual demand ÷ Economic order quantity × ordering cost per order + Economic order quantity ÷ 2 × carrying cost per unit

= 10,000 × $6.50 + 10,000 ÷ 5,000 × $150 + 5,000 ÷ 2 × $0.75

= $65,000 + 300 + $1,875

= $67,175

Therefore there will be 5 units should store at a time and cost of inventory is 300 + $1,875 = $2,175