Question

Bruno Fruscalzo decided to start a small production facility in Sydney to sell gelato to the local restaurants. His local milk supplier charges $0.5 per kg of milk plus a $25 delivery fee (that is independent of the amount ordered). Bruno’s holding cost is $0.02 per kg per month. He needs 9750 kgs of milk per month.

a.Suppose Bruno orders 9250 kgs each time. What is his average inventory (kgs)?

b.Suppose Bruno orders 7000 kgs each time. How many orders does he place with his supplier each year? not attempted orders

c.How many kgs should Bruno order from his supplier with each order to minimize the sum of ordering and holding costs?

d.If Bruno’s storage vessel can hold only 2000 kgs of milk, what would be Bruno’s annual ordering and holding costs?not attempted(Do not round intermediate calculations. Round your answer to 2 decimal places.)

e.If Bruno’s storage vessel can hold only 5000 kgs of milk, what would be Bruno’s annual ordering and holding costs?not attempted(Do not round intermediate calculations. Round your answer to 2 decimal places.)

f.Bruno’s supplier’s truck can carry 20,000 kgs of milk. The supplier does not want to deliver to more than 3 customers with each truck. Thus, the supplier requires a minimum order quantity of 6,500 kgs. If Bruno orders the minimum amount, what would be the sum of his annual ordering and holding costs? Assume he has a storage vessel large enough to hold 6,500 kgs.not attempted(Round your answer to 3 decimal places.)

g.Bruno’s supplier offers a 2% discount when a customer orders a full truck, which is 20,000 kgs. Assume Bruno can store that quantity and the product will not spoil. If Bruno orders a full truck, what would be the inventory holding and ordering cost incurred per kg of milk? Assume the discount also applies to the holding cost.not attempted

Answer 1

(c)
The order size should be the economic order quantity which is computed as:

Q = (2.d.K / h)1/2 = sqrt(2*9750*20 / 0.02) = 4937.10

(d)
If Q = 2000 kg,
Total cost of ordering + carrying = (12d/Q) * K + (Q/2) *12h = (12*9750/2000)*25 + (2000/2)*0.02*12 = $1702.5

(e)
If Q = EOQ = 4937.10 kg
Total cost of ordering + carrying = (12d/Q) * K + (Q/2) *12h = (12*9750/4937.10)*25+ (4937.10/2)*0.02*12 = $1184.90

(f)
If Q = 6,500 kg,
Total cost of ordering + carrying = (12d/Q) * K + (Q/2) *12h = (12*9750/6500)*25 + (6500/2)*0.02*12 = $1230

(g)
If Q = 20,000 kg,
Total cost of ordering + carrying = (12d/Q) * K + (Q/2) *12h = (12*9750/20,000)*25 + (20,000/2)*0.02*12 = $2546.25
So, per kg cost = 2546.25 / (9750*12) = $0.022