Question

The Ambrosia Bakery makes cakes for freezing and subsequent sale. The bakery, which operates five days a week, 52 weeks a year, can produce cakes at the rate of 116 cakes per day. The bakery sets up the cake-production operation and produces until a predetermined number (Q) have been produced. When not producing cakes, the bakery uses its personnel and facilities for producing other bakery items. The setup cost for a production run of cakes is $700. The cost of holding frozen cakes in storage is $9 per cake per year. The annual demand for frozen cakes, which is constant over time, is 6000 cakes. Determine the following:

Optimal production run quantity (Q)

Total annual inventory costs

Optimal number of production runs per year

Optimal cycle time (time between run starts)

Run length in working days

Answer 1

The student is asked to determine the optimal production run quantity, total annual inventory cost, optimal number of runs, cycle time, and run length for Ambrosia Bakery's frozen cakes, considering setup and holding costs, and constant annual demand.

Step-by-step explanation:

The objective is to find the optimal production run quantity (Q) for the Ambrosia Bakery considering the given cost structure and demand. To do this, we need to calculate the economic order quantity (EOQ), which is found by taking the square root of (2DS/H), where D is the annual demand, S is the setup cost or ordering cost, and H is the holding cost per unit per year.

Given the annual demand (D) of 6000 cakes, setup cost (S) of $700, and holding cost (H) of $9 per cake per year, we can calculate:

Q = sqrt((2 * 6000 * 700) / 9)

The total annual inventory costs include the sum of the setup costs and the holding costs. The setup cost for each run is $700, and since we know the demand, we can calculate the number of runs needed per year and multiply by the cost per run to get the total setup costs. The holding cost is calculated by taking the average inventory level (Q/2) multiplied by the holding cost per unit (H).

The optimal number of production runs per year is determined by dividing the annual demand (D) by the optimal production quantity (Q).

The optimal cycle time is the time between the start of one run and the start of the next, calculated by dividing the number of workdays per year by the number of runs per year.

The run length in working days is determined by dividing the optimal production quantity (Q) by the daily production rate.