Question

Bruno Fruscalzo decided to start a small production facility in Sydney to sell gelato to the local restaurants. His local milk supplier charges $0.50 per kg of milk plus a $15 delivery fee (the $15 fee is independent of the amount ordered). Bruno’s holding cost is $0.02 per kg per month. He needs 9,750 kg of milk per month.

a)Suppose Bruno orders 9000 kg each time. What is his average inventory (in kg)?
b)Suppose Bruno orders 7000 kg each time. How many orders does he place with his supplier each year?
c)How many kg should Bruno order from his supplier with each order to minimize the sum of the ordering and holding costs?

d)If Bruno’s storage vessel can hold only 3000 kg of milk, what would be Bruno’s minimum annual ordering and holding costs?

Answer 1

A. 4500kgs

B. 15.4orders

(c)

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

Q = (2.d.K / h)1/2 = sqrt(2*9000*20 / 0.03) = 3464.1 kg

(d)

If Q = 3000 kg,

Total cost of ordering + carrying = (12d/Q) * K + (Q/2) *12h = (12*9000/3000)*20 + (3000/2)*0.03*12 = $1,260

(e)

If Q = EOQ = 3464.1 kg

Total cost of ordering + carrying = (12d/Q) * K + (Q/2) *12h = (12*9000/3464.1)*20 + (3464.1/2)*0.03*12 = $1,247.1

(f)

If Q = 6,500 kg,

Total cost of ordering + carrying = (12d/Q) * K + (Q/2) *12h = (12*9000/6500)*20 + (6500/2)*0.03*12 = $1,502.3

(g)

If Q = 20,000 kg,

Total cost of ordering + carrying = (12d/Q) * K + (Q/2) *12h = (12*9000/20,000)*20 + (20,000/2)*0.03*12 = $3,708

So, per kg cost = 3708 / (9000*12) = $0.034

Step-by-step explanation:

Answer 2

A. 4500kgs

B. 15.4orders

(c)

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

Q = (2.d.K / h)1/2 = sqrt(2*9000*20 / 0.03) = 3464.1 kg

(d)

If Q = 3000 kg,

Total cost of ordering + carrying = (12d/Q) * K + (Q/2) *12h = (12*9000/3000)*20 + (3000/2)*0.03*12 = $1,260

(e)

If Q = EOQ = 3464.1 kg

Total cost of ordering + carrying = (12d/Q) * K + (Q/2) *12h = (12*9000/3464.1)*20 + (3464.1/2)*0.03*12 = $1,247.1

(f)

If Q = 6,500 kg,

Total cost of ordering + carrying = (12d/Q) * K + (Q/2) *12h = (12*9000/6500)*20 + (6500/2)*0.03*12 = $1,502.3

(g)

If Q = 20,000 kg,

Total cost of ordering + carrying = (12d/Q) * K + (Q/2) *12h = (12*9000/20,000)*20 + (20,000/2)*0.03*12 = $3,708

So, per kg cost = 3708 / (9000*12) = $0.034

Step-by-step explanation: