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The Ambrosia Bakery makes cakes for freezing and subsequent sale. The bakery operates five days a week, 52 weeks a year, and can produce cakes at a rate of 116 cakes per day. The bakery sets up the cake-production operation and produces until a predetermined number (Q) has been reached. When not producing cakes, the bakery uses its personnel and facilities for 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 is constant over time at 6000 cakes.

Determine the following:

a. Optimal production run quantity (Q)
b. Total annual inventory costs
c. Optimal number of production runs per year
d. Optimal cycle time (time between run starts)
e. Run length in working days

Answer :

The Ambrosia Bakery wants to determine the optimal production run quantity (Q) for cakes, considering setup costs, holding costs, and demand. Using the Economic Order Quantity (EOQ) formula, the optimal Q is calculated to be approximately 188 cakes. The total annual inventory cost, including setup costs and holding costs, amounts to $3,144. With the optimal Q, the bakery should conduct around 32 production runs per year, with each run lasting approximately 1.5625 working days.

Demand (D) = 6000 cakes per year

Setup cost (S) = $700 per production run

Holding cost (H) = $9 per cake per year

Production rate (P) = 116 cakes per day

Working days per year = 5 days per week * 52 weeks = 260 days

a. Optimal production run quantity (Q):

Q = sqrt((2 * D * S) / H) = sqrt((2 * 6000 * 700) / 9) ≈ 1354 cakes

b. Total annual inventory costs:

Total annual inventory costs = (Q/2) * H + (D/Q) * S = (1354/2) * 9 + (6000/1354) * 700 ≈ $3055.50 + $3085.66 ≈ $6141.16

c. Optimal number of production runs per year:

Number of production runs per year = D / Q = 6000 / 1354 ≈ 4.43 (round up to 5 runs)

d. Optimal cycle time (time between run starts):

Cycle time = 260 days / 5 runs ≈ 52 days

e. Run length in working days:

Run length = Q / P = 1354 / 116 ≈ 11.68 (round up to 12 working days)

Therefore, the optimal production run quantity is approximately 1354 cakes, the total annual inventory costs are around $6141.16, the optimal number of production runs per year is 5, the optimal cycle time is approximately 52 days, and the run length in working days is about 12 days.

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