Given Annual demand D = 800
Ordering cost S = 60
Holding cost H = 0.3*Price P
Economic order quantity EOQ
https://latex.codecogs.com/gif.latex?EOQ%3D%5Csqrt%7B%5Cfrac%7B2DS%7D%7BH%7D%7D
https://d2vlcm61l7u1fs.cloudfront.net/media%2F4f7%2F4f7efcb1-e523-4754-bb97-6dc59ae8680e%2FphpzI6WGg.png
If EOQ is with in the range it is feasible. EOQ 79 is in the range of 50-99. so it is feasible.
We calculate total costs at Q= 79 , 100,200 and 500.
Total cost = Annual purchase cost + Annual holding cost + Annual ordering cost = PD + (Q/2)H + (D/Q)S
Q
Purchase
cost
Annual
Holding cost
Annual
ordering
Cost
Total cost
79 =800*51.5=41200 =(79/2)*15.45=610.3 =(800/79)*60 = 607.6 =42417.9
100 =800*49.5=39600 =(100/2)*14.85=742.5 =(800/100)*60=480 =40822.5
200 =800*48=38400 =(200/2)*14.4=1440 =(800/200)*60=240 =40080
500 =800*47=37600 =(500/2)*14.1=3525 =(800/500)*60=96 =41221
Total cost is less at Q = 200
Order quantity Q = 200