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
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.
To determine the economic run size, we can use the Economic Order Quantity (EOQ) formula. The EOQ formula is given by:
EOQ = sqrt((2DS)/H)
Where:
D = Annual demand (in this case, monthly demand)
S = Ordering cost or setup cost per order
H = Holding cost per unit per time period
First, we need to calculate the annual demand:
Annual demand = Monthly demand x Number of months
Annual demand = 520 boxes x 12 months
Annual demand = 6240 boxes
Next, we can substitute the values into the EOQ formula:
EOQ = sqrt((2 x D x S) / H)
EOQ = sqrt((2 x 6240 x 66) / 1)
EOQ = sqrt(824,640 / 1)
EOQ = sqrt(824,640)
EOQ ≈ 907.83
Since the EOQ is the economic run size, we round it to the nearest whole number. Therefore, the economic run size is 908.
Among the options provided, none of them match the calculated economic run size of 908.