Question

Garden Variety Flower Shop uses 830 clay pots a month. The pots are purchased at $3.40 each. Annual carrying costs per pot are estimated to be 10 percent of cost, and ordering costs are $10 per order. The manager has been using an order size of 2,000 flower pots. a.What additional annual cost is the shop incurring by staying with this order size

Answer 1

a. The additional annual cost that the shop is incurring by staying with this order size is: $130.

b. The benefit for using the optimal order quantity yield is: 38.27%.

a. Additional annual cost  

Annual demand (D) =$830x 12= $9,960

Ordering cost=$10 per order

Annual carrying costs(H)=0.10 ×$3.40 = $0.34

Order Quantity(Q) = 2,000

Find TC for Q

TC=Q÷2×H + D÷Q × S

TC=2,000÷2 × $0.34 + $9,960÷2,000×$10

TC=$340+$49.8

TC=$389.8............. (1)

Now find Qo

Qo=√2DS÷H

Qo=√2×$9,960×$10÷0.34

Qo=√585,882.352941

Qo=$765.429522

Qo=$765.43(Approximately)

Find TC for Qo  

TC=Q÷2×H + D÷Q ×

TC=765.43÷2 × $0.34 + $9,960÷765.43×$10

TC=$130.12+$130.12

TC=$260.24................(2)

Now let determine the additional annual cost

Additional annual cost=$389.8-$260.24

Additional annual cost=$129.56

Additional annual cost=$130 (Approximately)

b. Benefit for using the optimal order quantity yield (relative to the order size of 2,000)

Benefit=Qo÷Q

Benefit=$765.43÷2,000×100

Benefit=38.27%

Inconclusion the additional annual cost is $130 and optimal order quantity yield is 38.27%.

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