Question

1. A shop that makes candles offers a scented candle, which has a monthly demand of 360 boxes. Candles can be produced at a rate of 36 boxes per day. The shop operates 20 days a month. Assume that demand is uniform throughout the month. Setup cost is $60 for a run, and holding cost is $2 per box on a monthly basis.

Determine the following:
(A) the economic run size
(B) the maximum inventory
(C) the number of days in a run
The daily usage rate (u) is 18 boxes. The daily production rate (p) is 36 boxes.
2. A manager has prepared a forecast of expected aggregate demand for the next six months. Develop an aggregate plan to meet this demand given this additional information: A level production rate of 100 units per month will be used. Back orders are allowed, and they are charged at the rate of $8 per unit per month. Inventory holding costs are $1 per unit per month in ending inventory. Determine the cost of this plan if regular time cost is $20 per unit and beginning inventory is zero.

Answer 1

The economic run size is approximately 208 boxes. The maximum inventory is approximately 116 boxes. The number of days in a run is approximately 5.78 days.

Step-by-step explanation:

(A) Economic Run Size:

To determine the economic run size, we can use the Economic Order Quantity (EOQ) formula:
EOQ = √((2DS)/H), where D is the annual demand, S is the setup cost per order, and H is the holding cost per unit per year. Given that the monthly demand is 360 boxes, the setup cost is $60, and the holding cost is $2 per box per month, we can calculate the EOQ as follows:
EOQ = √((2*360*60)/2) = √(43200) = 207.86
Therefore, the economic run size is approximately 208 boxes.

(B) Maximum Inventory:

To determine the maximum inventory, we can multiply the economic run size (EOQ) by the number of runs in a month. Since candles can be produced at a rate of 36 boxes per day and the shop operates 20 days a month, the number of runs in a month is 20/36 ≈ 0.56 runs. Multiplying the economic run size by this number, we get: 208 * 0.56 = 116.48
Therefore, the maximum inventory is approximately 116 boxes.

(C) Number of Days in a Run:

To determine the number of days in a run, we can divide the economic run size (EOQ) by the daily production rate. Dividing 208 boxes by 36 boxes per day, we get: 208 / 36 ≈ 5.78
Therefore, the number of days in a run is approximately 5.78 days.

Answer 2

1. The economic run size is 104.

2. The maximum inventory is 208

3. The number of days in a run is 3.

Economic run size refers to the optimal production quantity that minimizes overall production costs.

The economic run size will be computed using Economic production quantity (EPQ) formula :

`Q = √(2SD / H*(1-(u/p))\\= \sqrt{(2*360*60)/(2 * (1-18/36))`

= 103.923048454

= 104

The maximum inventory (MI) is given by :

MI = Qp / u

= 104 * 36 / 18

= 208

The number of days in a run (N) is

N = 104 /36

= 2.88888888889

= 3.