To find the economic run size, we can use the Economic Order Quantity (EOQ) formula:
EOQ = √((2DS) / H)
Where:
D = Annual demand (Monthly demand * 12)
S = Setup cost per run
H = Holding cost per unit per year (Monthly holding cost * 12)
Given:
Monthly demand = 520 boxes
Production rate = 34 boxes per day
Operating days per month = 20 days
Setup cost = $66
Holding cost = $1 per box per month
First, let's find the annual demand:
Annual demand = Monthly demand * 12
Annual demand = 520 * 12
Annual demand = 6,240 boxes
Next, let's find the setup cost per run:
Number of production runs per month = (Annual demand) / (Production rate per day * Operating days per month)
Number of production runs per month = 6,240 / (34 * 20)
Number of production runs per month ≈ 9.18
Since we cannot have fractional runs, we round it up to 10 runs per month.
Setup cost per run = Total setup cost / Number of production runs per month
Setup cost per run = $66 / 10
Setup cost per run = $6.60
Now, let's find the holding cost per unit per year:
Holding cost per unit per year = Holding cost per unit per month * 12
Holding cost per unit per year = $1 * 12
Holding cost per unit per year = $12
Now we can calculate the economic run size using the EOQ formula:
EOQ = √((2DS) / H)
EOQ = √((2 * 6,240 * $6.60) / $12)
EOQ = √(82,944 / $12)
EOQ ≈ √6,912
EOQ ≈ 83
Therefore, the economic run size is approximately 83 boxes. None of the given options (a, b, c, d) match this value.
a shop that makes candles offers a scented candle, which has a monthly demand of 520 boxes. candles can be produced at a rate of 34 boxes per day. the shop operates 20 days a month. assume that demand is uniform throughout the month. setup cost is $66 for a run, and holding cost is $1 per box on a monthly basis. determine the the economic run size: a. 128 b. 541 c. 1114 d. 262
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