Question

The demand for a detector 2LCH Co. sells uoo units1 art.Cost of +he detector is 4o0 $ per unt. Corruing costs are 25:/ of the unit cost, and ordeing costs are 50 $ per order. 21LCH Co. is given a guontity discOunt of 10:1., if they place a minimum orcler of 200 detectonrs. Should 2ILCH CO with relevant calculations. quantity take the dis count ) Prove point your 'a) Calculate the optimal order quantity, and the total cost of the model.

Answer 1

a) Optimal order quantity or EOQ= √(2AO)/C

Annual demand (A)- 400units 1qtr. Which means 400×4=1600units

Detector cost is $400 per unit

Ordering cost (O)=$50

Carrying Cost is 25%of unit cost (C) = ($400×25%)

EOQ=√(2×1600×50)/100 =√1600=40units.

Total cost = Annual ordering cost + Annual Carrying Cost

Total cost = (Demand× ordering cost)/quantity + (carrying Cost ×quantity)/2

Total Cost = (1600×$50)/40+(40×100)/2=$200+$2,000=$2,200

b) here EOQ=40 units

Discount order quantity (DOQ) =200units

Annual order under EOQ= Demand/EOQ= 1600/40=40 orders

Annual order under DOQ= Demand /DOQ= 1600/200= 8 orders

Annual inventory under EOQ= EOQ/2=40/2= 20 units

Annual inventory under DOQ=DOQ/2=200/2=100 units

1) Saving from reduction in price

Discount is 10%

Demand ×Price×discount = 1600×$400×0.10=$64,000

2) Saving from reduction in order= orders reduced× order cost

= (40-8)×$50=32×$50=$1,600

3) Increasing in carrying Cost

=Increase in average inventory × carrying Cost

=(100-20)×$100=80×100=$8,000

Net effects on income = saving from reduction in price + saving from reduction in order - increasing in carrying Cost

Net effects on income = $64,000+$1,600-$8,000= $57,600

As the net effect on income is positive the store should avail the quantity discount on detectors.