Question

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 11,500 flashing lights per year and has the capability of producing 100 per day. Setting up the light production costs $51. The cost of each light is $1.00. The holding cost is $0.5 per light per year.

a. What is the optimal size of the production run? (answer 6,168)

b. What is the average holding cost per year? (answer 95.60)

c. What is the average setup cost per year? (answer 95.09)

d. What is the total cost per year, including the cost of lights? (answer 11690.69)

Answer 1

Note: The answers written in the brackets are for holding cost of $ 0.05 but in the question, the Holding cost mentioned is $ 0.5. Therefore, I am correcting all the answers for you. In case of any doubt, please mention it in the comment. Thank you

Annual demand (D) = 11,500 units

Number of working days = 300

Daily demand (d) = 11500/300

Daily demand (d) = 38.3333 units

Cost of each light (C) = $ 1

Setup Cost (S) = $ 51

Holding cost (H) = $ 0.5

Daily production (p) = 100 units

(A)

POQ = 1950.47 units

POQ (Q*) = 1950 units (rounded off to nearest whole number)

Therefore, optimal size of Production run = 1950 units

(B)

Average Holding cost = (Q*/2) × [1 - (d/p)] × H

Average Holding cost = (1950/2) × [1 - (38.333/100) × 0.5

Average Holding cost = $ 300.625

(C)

Average set up cost = (D/Q) × S

Average set up cost = (11500/1950) × 51

Average set up cost = $ 300.769

(D)

Total cost per year = Annual Holding cost + Average set up cost + D × C

Total cost per year = $ 300.625 + $ 300.769 + (11500 × 1)

Total cost per year = $ 12,101.394