Question

Cesar Rego​ Computers, a Mississippi chain of computer hardware and software retail​ outlets, supplies both educational and commercial customers with memory and storage devices. It currently faces the following ordering decision relating to purchases of​disks:

D	37,000 disks
S	​$23
I	23​%
Purchase price	​$0.88
Discount price	​$0.82

Quantity needed to qualify for the discount​ = 5,900 disks.

What is the​ EOQ?

EOQ​ = ___ units ​(round your response to the nearest whole​number).

Since the total cost with discounted volume is (greater than or equal to/ less than?) the total cost at the EOQ​ volume, Cesar Rogo should (take or not take)

the​ discount, provided other factors such as storage​ space, etc. permits.

Answer 1

DEMAND = 37000
ORDERING COST = 23
HOLDING COST = 0.2024
COST PER UNIT = 0.88

EOQ = SQRT(2 * ANNUAL DEMAND * ORDERING COST / HOLDING COST PER UNIT) = SQRT(2 * 37000 * 23 / 0.2024) = 2900

ANNUAL HOLDING COST = (EOQ / 2) * HOLDING COST PER UNIT = (2900 / 2) * 0.2024 = 293.48

ANNUAL ORDERING COST = (DEMAND / EOQ) * ORDERING COST = (37000 / 2900) * 23 = 293.45

ANNUAL MATERIAL COST = ANNUAL DEMAND * PRICE PER UNIT = 37000 * 0.88 = 32560

TOTAL COST OF INVENTORY = ANNUAL HOLDING COST + ANNUAL ORDERING COST + ANNUAL MATERIAL COST = 293.48 + 293.45 + 32560 = 33146.93

USING 5900 UNITS AS ORDERING QUANTITY

ANNUAL HOLDING COST = (5900 / 2) * 0.1886 = 556.37
ANNUAL ORDERING COST = (37000 / 5900) * 23 = 144.24
TOTAL COST OF PURCHASING = 37000 * 0.82 = 30340
ANNUAL TOTAL COST = ANNUAL HOLDING COST + ANNUAL ORDERING COST + ANNUAL COST OF MATERIAL = 556.37 + 144.24 + 30340 = 31040.61

OPTIMAL ORDER QUANTITY = 5900 UNITS

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