# 1. Using the data below, find the least-cost order quantities when there are quantity discounts (order cost = \$60, inventory holding cost = 30 percent of item value, and annual demand = 800): ​Quantity Ordered price fewer than 50 units \$53 50-99 units \$51.50 ​100-199 units 49.50 ​200-499 units \$48 ​More than 499 units \$47

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

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