Question

1). A local nursery, greens used 30,000 bags of plan food annually. It cost $10 to place an order for plant food. It’s annual holding cost per unit is 25% of the unit price. In an effort to reduce its inventory. Rapid grower is offering greens two additional al price breaks to consider. If green orders at least 390 units, the price per bag is $15. If green orders at least 780 units, the price per bag is $12. What is your EOQ calculation when unit price is $12? Is it feasible?

A: 447.21; not feasible

B: 447.21; feasible

C: 500; feasible

D: 500; not feasible

E: 489.90; not feasible

2). A local nursery, greens used 30,000 bags of plan food annually. It cost $10 to place an order for plant food. It’s annual holding cost per unit is 25% of the unit price. In an effort to reduce its inventory. Rapid grower is offering greens two additional al price breaks to consider. If green orders at least 390 units, the price per bag is $15. If green orders at least 780 units, the price per bag is $12. What is your EOQ calculation when unit price is $15? Is it feasible?

A: 447.21; not feasible

B: 447.21; feasible

C: 500; feasible

D: 500; not feasible

E: 489.90; not feasible

3). A local nursery, greens used 30,000 bags of plan food annually. It cost $10 to place an order for plant food. It’s annual holding cost per unit is 25% of the unit price. In an effort to reduce its inventory. Rapid grower is offering greens two additional al price breaks to consider. If green orders at least 390 units, the price per bag is $15. If green orders at least 780 units, the price per bag is $12. What is the total cost for the order quantity that is most cost efficient?

A: 452750

B: 301885.10

C: 114000

D: 451500

E: 361554.6

Answer 1

1). A local nursery, greens used 30,000 bags of plan food annually. It cost $10 to place an order for plant food. It’s annual holding cost per unit is 25% of the unit price. In an effort to reduce its inventory. Rapid grower is offering greens two additional al price breaks to consider. If green orders at least 390 units, the price per bag is $15. If green orders at least 780 units, the price per bag is $12. What is your EOQ calculation when unit price is $12? Is it feasible?

Formula to calculate optimal order quantity is economic order quantity (EOQ)

EOQ = Q = √ (2 * Annual Demand * Ordering cost/ Inventory holding cost)

Where,

Annual demand, D = 30,000 bags

Ordering cost S = $10 per order

Cost of Bag = $12

Annual Inventory holding cost rate H = 25% of cost = 25% * $12 = $3 per unit per year

Therefore

EOQ = Q = √ (2 * 30,000 *$10 / $3) = 447.21

Optimal order quantity or economic order quantity is 447.21 units but it is not feasible because at the price of $12 per bag, order quantity should be at least 780 units

Therefore correct answer is option: A: 447.21; not feasible

2). A local nursery, greens used 30,000 bags of plan food annually. It cost $10 to place an order for plant food. It’s annual holding cost per unit is 25% of the unit price. In an effort to reduce its inventory. Rapid grower is offering greens two additional al price breaks to consider. If green orders at least 390 units, the price per bag is $15. If green orders at least 780 units, the price per bag is $12. What is your EOQ calculation when unit price is $15? Is it feasible?

Formula to calculate optimal order quantity is economic order quantity (EOQ)

EOQ = Q = √ (2 * Annual Demand * Ordering cost/ Inventory holding cost)

Where,

Annual demand, D = 30,000 bags

Ordering cost S = $10 per order

Cost of Bag = $15

Annual Inventory holding cost rate H = 25% of cost = 25% * $15 = $3.75 per unit per year

Therefore

EOQ = Q = √ (2 * 30,000 *$10 / $3.75) = 400

Optimal order quantity or economic order quantity is 400 units but it is feasible because at the price of $15 per bag, order quantity should be at least 390 units

No option is correct answer.

3). A local nursery, greens used 30,000 bags of plan food annually. It cost $10 to place an order for plant food. It’s annual holding cost per unit is 25% of the unit price. In an effort to reduce its inventory. Rapid grower is offering greens two additional al price breaks to consider. If green orders at least 390 units, the price per bag is $15. If green orders at least 780 units, the price per bag is $12. What is the total cost for the order quantity that is most cost efficient?

Total inventory cost = total ordering cost + total carrying cost + cost of material

Total cost of operation = (D/Q)* S + (H*Q)/2 + D * Purchase price

= (30000/400)*10 + ($3.75*400)/2 + 30000 * $15 = $451,500

Where optimum order size is Q =400 units

Total cost of operation at this optimal order is $451,500

Total cost of operation = (D/Q)* S + (H*Q)/2 + D * Purchase price

= (30000/780)*10 + ($3*780)/2 + 30000 * $12 = $361,554.60

Where optimum order size is Q =780 units

Total cost of operation at this optimal order is $361,554.60 (this quantity is most cost efficient as total cost is lower at this)

Therefore correct answer is option: E: 361554.6