High School

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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:

1. Optimal production run quantity (Q)
2. Total annual inventory costs
3. Optimal number of production runs per year
4. Optimal cycle time (time between run starts)
5. Run length in working days

Answer :

Final answer:

The Ambrosia Bakery's optimal production run quantity is approximately 3055 cakes, with total annual inventory costs that include setup and holding costs; the bakery should have roughly 2 production runs per year and an optimal cycle time of about 182.5 days between runs. The run length would be approximately 26.34 working days.

Explanation:

The Ambrosia Bakery's problem can be approached using the Economic Order Quantity (EOQ) model and the concept of inventory management within operations management. The optimal production run quantity (Q) can be calculated using the formula:

EOQ = sqrt((2DS)/H), where
D = Demand rate (6000 cakes/year),
S = Setup cost ($700), and
H = Holding cost per unit per year ($9).

Calculating, we find that the optimal production quantity Q is:

EOQ = sqrt((2 * 6000 * 700)/9) = sqrt(9333333.33) ≈ 3055 cakes.

The total annual inventory costs include the setup costs and the holding costs which can be calculated as follows:

Total setup costs = (D/Q) * S, and the
Total holding costs = (Q/2) * H.

The optimal number of production runs per year is D/Q, which in this case is 6000/3055 ≈ 1.96 or 2 runs when rounded up.

The optimal cycle time, which is the time between the starts of production runs, is 1 / (D/Q) in years or 365 / (D/Q) in days. As such, the optimal cycle time is 365 / 2 = 182.5 days.

Lastly, the run length in working days is the time taken to produce Q cakes at the production rate of 116 cakes/day, computed as Q / Production rate. Therefore, the run length is 3055 / 116 ≈ 26.34 days.

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Rewritten by : Barada

Final answer:

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.

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.