Question

Sarah owns and operates a small factory that manufactures plastic bottles which she sells to

bottling companies.

Additional information:

Annual demand is 1 million bottles spread evenly over the year

Setup cost is $5000 per batch

Holding cost is $3 per annum for each bottle

Maximum production capacity is 2 million bottles per annum

Currently, bottles are manufactured in 10 batches

A. Find the optimum production quantity that Sarah should produce to minimize her costs

B. Calculate the current annual holding cost and setup cost​

Answer 1

Answer:

plastic bottles which she sells to

bottling companies.

Additional information:

Annual demand is 1 million bottles spread evenly over the year

Setup cost is $5000 per batch

Holding cost is $3 per annum for each bottle

Maximum production capacity is 2 million bottles per annum

Currently, bottles are manufactured in 10 batches

A. Find the optimum production quantity that Sarah should produce to minimize her costs

B. Calculate the current annual holding cost and setup cost

Answer 2

Answer:

Concept :

The order size of a production batch that minimises the overall cost is referred to as the economic batch quantity (EBQ), sometimes known as the optimum production quantity.Additionally, batch production lessens the risk of obsolescence since modest adjustments to product specifications can be made in subsequent batches in response to consumer or retailer input rather than creating everything at once and crossing one's fingers. When manufacturing is done internally and any raw materials or parts needed for production are either acquired internally or are supplied incrementally by other companies according to the production requirement, EBQ is used to determine the size of a production run, whereas EOQ is suitable for determining the order size when the parts, materials, or finished goods are ready to be delivered by external suppliers when the order is placed.

Explanation:

A. Find the optimum production quantity that Sarah should produce to minimize her costs.

Economic Batch Quantity  = √((2×Cs×D)/(Ch(1-D)/P)))

Where,

Cs is the batch setup cost.

D is the yearly demand.

P is the production capacity per year.

Ch represents the annual expense of keeping one finished item in stock.

 =  √((2×5000×1,00,000)/(3×(1-(1,00,000/2,000,000))))

 =  √(10,000,000,000/1.5)

 = √6,666,666,666

 =  81,650

Batches of 81,650 bottles should be produced by Sarah.

B. Calculate the current annual holding cost and setup cost​

Batch quantity = $\frac{Annual demand}{Number of batches}$

= $\frac{1000000}{10}$

= 100,000 units

Annual holding cost = $\frac{batch quantity}{2}$ × Ch × $\frac{1 - D}{P}$

= $\frac{1000000}{2}$ × 3 × (1- $\frac{1000000}{2000000}$)

= 75,000.

Setup cost = Number of stepups × setup cost

= 10×5000

= 50,000.

Total current cost = 75,000 + 50,000

= 1,25,000.

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