Please provide solution and explanation in detail....can\'t use Excel, only scie

Question

Please provide solution and explanation in detail....can't use Excel, only scientific calculator, if needed. Thanks so much!

A toy manufacturer uses approximately 42,000 silicon chips annually. The chips are used at a steady rate during 250 working days a year. The annual holding cost is $3 per chip, ordering cost is $120, and lead time is 3 days. Currently production manager uses order quantity of 3000 units. Determine:

a- The Economic Order Quantity (EOQ).

b- the cost saving if company uses EOQ instead of current order quantity of 3000 units.

c- find the basic reorder point (expected demand during lead time)

d- find reorder point if demand during lead time has normal distribution with standard deviation of 7 and we desire only 5% chance of stock out. (HINT ROP=expected demand during lead time + Safety stock).

Explanation / Answer

Answer:

a.

Economic Order Quantity (EOQ) = ((2*Annual demand*ordering cost)/holding cost)^.5

EOQ = (2*42000*120/3)^.5

EOQ = 1833.03 or 1833 units of silicon chips

b.

Cost when order quantity is 3000 = Total ordering cost + total holding cost

Cost when order quantity is 3000 = (42000/3000)*120 + (3000/2)*3 = $6180

Cost when order quantity is 1833(EOQ) = (42000/1833)*120 + (1833/2)*3 = $5499.09

Thus, savings when EOQ is ordered = 6180 – 5499.09 = $680.9 or $681 approx.

c.

Basic Reorder point = Daily demand*Lead time = (42000/250)*3 = 504 units of silicon chips

d.

Reorder point = Daily demand*Lead time + Z*SD*(Lead Time)^.5

At 5% chance, value of Z = 1.65 (As per Z table)

Thus,

Reorder point = (42000/250)*3 + 1.65*7*3^.5

Reorder point = 524 units of silicon chips

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