Answer to Question #165157 in Financial Math for sally

Question

Alyce operates a factory that manufactures pencil boxes which she sells to stationery store.

Additional information:

Annual demand is 1 million pencil boxes per year

Setup cost is $5000 per batch

Holding cost is $3 per year for each pencil boxes

Maximum production capacity is 2 million pencil boxes per year

Currently, pencil boxes are manufactured in 10 batches.

1 a) Find the optimum production quantity that Alyce should produce to minimize her costs.

Economic Batch Quantity

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

= √(10,000,000,000 / 1.5)

= 81,650

   b) Calculate the current annual holding cost and setup cost. 

Batch Quantity = Annual Demand ÷ Number of batches

= 1,000,000 ÷ 10

= 100,000 units

Annual Holding Cost 

= (100,000/2) × 3 × (1-(1,000,000/2,000,000))

= $75,000

Setup Cost

= 10 × 5000

= $50,000

Total Current Cost = ($75,000 + $50,000) = $125,000

  c) Draw a diagram showing stock level for the first batch, assume 1 year has 250 working days 

Answer 1

Diagram for stock level: