Adovilsky Manufacturing Company, in Hayward, California, makes flashing lights for toys. The company operates its production facility 300300 days per year. It has orders for about 11 comma 80011,800 flashing lights per year and has the capability of producing 9595 per day. Setting up the light production costs $4848. The cost of each light is $0.950.95. The holding cost is $0.100.10 per light per year. 1. What is the optimal size of the production run?
2. What is the average holding cost per year?
3. What is the average setup cost per year?
4. What is the total cost per year, including the cost of the lights?

1. 5,231 units

2. $156 per year

3. $108 per year

4. $11,474

Explanation:

Here

D is Annual Demand which is 11,800 units per year

O is ordering cost and is $48 per setup

H is the holding cost per unit per year which is $0.1 per unit per year

P is production rate per year = 95 units per day * 300 days = 28,500 units

Now here,

1. Optimal Size (Production Run) = Sqaureroot [2OD *  1 / H * (1 - D/P)]

By putting values, we have:

Optimal Size of Production Run = Sqrt [2* $48* 11,800 Units* 1 / 0.1* (1 - 11,800/28,500)]    = 5,231 units

2. Average Total Holding Cost per year = H * (1 - D/P) * Q / 2

Here

Q is the Optimal Size of Production Run

By putting values, we have:

Average Total Holding Cost per year = $0.1 * (1 - 11,800/28,500) * 5,321 / 2

= $156 per year

3. Average Set up Cost per year = D / Q      * O

By putting values, we have:

Average Set up Cost per year = 11,800 / 5,231   *   $48 per setup

= $108 per year

4. Total Cost per Year = Average Total Holding Cost per year  + Average Set up Cost per year  + Total cost of purchase of 11,800 units

By putting values, we have:

Total Cost per Year = $156   +  $108  + 11,800 * $0.95

= $11,474

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