Answer to Question #164740 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.

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

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

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

      days 

Answer 1

Given,

Set up cost, $C_s=$ 5000$

Holding cost, $C_h=3$ $

Maximum capacity, $P=2,000,000$

Annual producing capacity, $D=1,000,000$

Solution A: Optimum Production Quantity

Economic Batch Quantity

$= \sqrt{ \dfrac{(2 \times C_s \times D)}{C_h(1 - \dfrac{D}{P})}}$

$= \sqrt{ \dfrac{(2 × 5000× 1,000,000)}{3 (1-\dfrac{(1,000,000)}{2,000,000)})}}$

$= \sqrt{ \dfrac{(10,000,000,000)}{1.5}}$

$= \sqrt{6,666,666,666}$

$= 81,650$ units

Alyce should manufacture bottles in batches of $81,650 \text{units}.$

Solution B: Current Costs

Batch Quantity = Annual Demand ÷ Number of batches

 $= 1,000,000 ÷ 10 = 100,000 units$

Annual Holding Cost =$\dfrac{\text{(Batch Quantity}}{2}) × C_h × (1- \dfrac{D}{P})$

 $= (\dfrac{100,000)}{2} × 3 × (1-\dfrac{(1,000,000)}{2,000,000)}$

$= 75,000$ $

Setup Cost = Number of setups × setup cost

 $= 10 × 5000 = 50,000$ $

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

Solution C: Savings from EBQ

Annual Holding Cost:

 $= \dfrac{\text{(Batch Quantity}}{2}) × Ch × (1- \dfrac{D}{P})$

 $= \dfrac{(81,650)}{2} × 3 × (1-\dfrac{(1,000,000)}{2,000,000})$

$= 61,238$ $

Setup Cost:

Number of batches $= 1,000,000 ÷ 81,650 = 12.2475$

Setup Cost = Number of batches × Cost of setup

$= 12.2475 × 5000 = 61,23 (B)$

Total Cost (EBQ) $= (A) + (B) = 122,476 (C)$

Total Current Cost $= 125,000 (D)$

Savings $= (D) - (C) = 2,524$ $

With increasing time the stock level of pencil boxes increasing. Stock diagram is given by