Question

explination of answers please so i can undeestand

.. 12.19 Radovilsky Manufacturing Company, in Hayward, California, makes flashing lights for toys. The company operates its production facility 300 days per year. It has orders for about 12,000 flashing lights per year and has the capability of producing 100 per day. Setting up the light production costs $50. The cost of each light is $1. The holding cost is $0.10 per light per year. a) What is the optimal size of the production run? b) What is the average holding cost per year? c) What is the average setup cost per year? d) What is the total cost per year, including the cost of the lights? PX

Answer 1

ANNUAL DEMAND = 12000

SETUP COST = 50

HOLDING COST = 0.1

DAILY PRODUCTION = 100

DAILY USAGE = DAILY USAGE = 12000 / 300 = 40

UNIT COST = 1

1. EPQ = SQRT(2 * DEMAND * SETUP COST / HOLDING COST) * SQRT(DAILY PRODUCTION / DAILY PRODUCTION - DAILY USAGE) = SQRT(2 * 12000 * 50 / 0.1) * SQRT(100 / 100 - 40) = 4472(ROUNDED)

2. MAXIMUM INVENTORY = (Q / DAILY PRODUCTION) * (DAILY PRODUCTION - DAILY USAGE)

(4472 / 100) * (100 - 40) = 2683(ROUNDED TO NEAREST WHOLE NUMBER)

AVERAGE INVENTORY = MAXIMUM INVENTORY / 2

2683 / 2 = 1342(ROUNDED TO NEAREST WHOLE NUMBER)

ANNUAL HOLDING COST = MAX INVENTORY / 2 * HOLDING COST

2683 / 2 * 0.1 = 134.15

3. ANNUAL SETUP COST = DEMAND / Q * SETUP COST

12000 / 4472 * 50 = 134.17

4. ANNUAL PURCHASE COST = COST PER UNIT * ANNUAL DEMAND = 1 * 12000 = 12000

TOTAL PURCHASE COST = ANNUAL HOLDING COST + ANNUAL ORDERING COST + ANNUAL PURCHASE COST = 134.15 + 134.17 + 12000 = 12268.32

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