Question

Master Hatter's demand for hats is 8,000 per year. The order cost (S) is $100 and the carrying cost (H) is $2.50 per unit. The cost paid (price) to the hat manufacturer is $15 per hat. 1. Compute the Economic Order Quantity 2. The supplier has indicated that Master Hatter can have a price of $14 per hat if he orders at least 1000 at a time. In order to minimize total costs (inventory plus purchase costs), Master Hatter should order XX? hats and will save XX dollars each year (do not round - enter dollars and cents).

Answer 1

DEMAND = 8000
ORDERING COST = 100
HOLDING COST = 2.5
COST PER UNIT = 15

EOQ = SQRT(2 * DEMAND * ORDERING COST / HOLDING COST) = SQRT(2 * 8000 * 100 / 2.5) = 800

ANNUAL HOLDING COST = (EOQ / 2) * HOLDING COST = (800 / 2) * 2.5 = 1000

ANNUAL ORDERING COST = (DEMAND / EOQ) * ORDERING COST = (8000 / 800) * 100 = 1000

ANNUAL MATERIAL COST = ANNUAL DEMAND * PRICE PER UNIT = 8000 * 15 = 120000

TOTAL COST OF INVENTORY = ANNUAL HOLDING COST + ANNUAL ORDERING COST + ANNUAL MATERIAL COST = 1000 + 1000 + 120000 = 122000

2. FOR 1000 UNITS AS THE Q

ANNUAL HOLDING COST = (EOQ / 2) * HOLDING COST = (1000 / 2) * 2.5 = 1250

ANNUAL ORDERING COST = (DEMAND / EOQ) * ORDERING COST = (8000 / 1000) * 100 = 800

ANNUAL MATERIAL COST = ANNUAL DEMAND * PRICE PER UNIT = 8000 * 14 = 112000

TOTAL COST OF INVENTORY = ANNUAL HOLDING COST + ANNUAL ORDERING COST + ANNUAL MATERIAL COST = 1250 + 800 + 112000 = 114050

3. SAVINGS = 120000 - 114050 = 5950