Question

Bell Computers purchases integrated chips at $350 per chip. The holding cost is 35 percent of the unit price per year, the ordering cost is $120 per order and sales are steady at 5,000 per year. The company’s supplier, Rich Blue Chip Manufacturing Inc., decides to offer price discounts to attract larger orders. The price structure is shown below:

**Quantity
Purchases
Price/Unit**

1-99 units $350

100-199 units $325

200 or more units $300

What is the optimal order quantity?

Answer #1

Annual demand D = 5000

Ordering cost S = 120

Holding cost = 0.35

Quantity range | Price C | Holding cost H |

1-99 | 350 | 0.35*350 = 122.5 |

100-199 | 325 |
0.35*325 = 113.75 |

200 or more | 300 |
0.35*300 = 105 |

We calculate EOQ for all the ranges

H = 122.5

EOQ = 99 units

It is feasible as it is with in the range

H = 113.75

EOQ = 103 units

It is feasible as it is with in the range

H = 105

EOQ = 107

It is not feasible but we get more discount. So we calculate total cost at Q = 99, Q = 103 and Q = 200

Total cost = Purchasing cost + Annual holding cost + Annual ordering costs = CD+(Q/2)H + (D/Q)S

Q = 99

Total cost = (350*5000)+(99/2)*122.5 + (5000/99)*120 = 1762124.36

Q = 103

Total cost = (325*5000)+(103/2)*113.75 + (5000/103)*120 = 1636683.37

Q = 200

Total cost = (300*5000)+(200/2)*105 + (5000/200)*120 = 1513500

Total cost is less at Q = 200 units

**Optimal order quantity = 200**

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