Question

Assume that the following quantity discount schedule is appropriate. If annual demand is 120 units, order costs are $20 per order, and the annual holding cost is 25% of price, what order quantity would you recommend?

Order Size                   Unit Cost

            0 to 49                       $30.00

            50 to 99                       $28.50

            100 or more                $27.00

Answer 1

Given

Annual demand D = 120

Ordering cost S = 20

Holding cost H = 25% of price

Range	Cost C	Holding cost H	EOQ
0 to 49	30	=30*0.25 = 7.5		Feasible
50 to 99	28.5	= 28.5*0.25 = 7.125		Not feasible
100 or more	27	= 27*0.25 = 6.75		Not feasible

First is Feasible because it is with in the range of 0 to 49 and and the remaining are not feasible because EOQ is not with in the range of 50 to 99 and 100 or more. So 25 is the order quantity but we are not getting more discount. So we calculate total cost at Q = 25, Q = 50 and Q = 100

Total cost = Total purchase cost + Annual holding cost + Annual ordering cost = CD + (Q/2)H + (D/Q)S

At Q = 25

Total cost = 30*120 + ( 25/2)*7.5 + (120/25)*20 = 3789.75

At Q = 50

Total cost = 28.5*120 + ( 50/2)*7.125 + (120/50)*20 = 3646.125

At Q = 100

Total cost = 27*120 + ( 100/2)*6.75 + (120/100)*20 = 3601.5

Total cost is less at Q = 100

So I recommend order quantity of 100