Answer:
Check the following calculations
Explanation:
Given Weekly demand = 250 gallons
Annual demand D = 250 gallons * 52 weeks per year = 13000 per year
Cost C = $1.20
Ordering cost = $35
Annual holding cost H = 35% of price = 0.35*1.2 = $0.42
a) Given order quantity Q = 1000 gallons
average inventory in gallons = Q/2 = 500 gallons
b) Q = 1500
No of orders per year = D/Q = 13000/1500 = 8.67 or 9 (round off)
c) Optimal order quantity Q
Q=\sqrt{2DS/H}
Q=\sqrt{(2*13000*35)/0.42}
Q=1472 GALLONS
d)
Q=2500
Annual Holding cost = (Q/2)H = (2500/2)0.42 = $525
Annual ordering cost = (D/Q)S = (13000/2500)35 = $182
Annual Holding cost + Annual ordering cost = 525 + 182 = $707
Average inventory in gallons = 500 gallons,
No of orders per year = 9
Optimal order quantity Q = 1472 Gallons
Optimal order quantity Q = 1472 Gallons
Sum of the ordering and holding costs per gallon will be $707.
Given data
Weekly demand = 250 gallons
Annual demand D = 250 gallons * 52 weeks per year = 13000 per year
Cost C = $1.20
Ordering cost = $35
Annual holding cost H = 35% of price = 0.35*1.2 = $0.42
Given order quantity Q = 1000 gallons
Average inventory in gallons = Q/2
Average inventory in gallons = 1000/2
Average inventory in gallons = 500 gallons
Given that Q = 1500
No of orders per year = D/Q
No of orders per year = 13000/1500
No of orders per year = 8.67 or 9
Optimal order quantity Q = [tex]\sqrt{{2DS/H}}[/tex]
Optimal order quantity Q = [tex]\sqrt{(2*13000*35)/0.42}}[/tex]
Optimal order quantity Q = 1472 Gallons
Given data Q=2500
Annual Holding cost = (Q/2)H
Annual Holding cost = (2500/2)0.42
Annual Holding cost = $525
Annual ordering cost = (D/Q)S
Annual ordering cost= (13000/2500)35
Annual ordering cost= $182
Annual Holding cost + Annual ordering cost
= 525 + 182
= $707
Hence, the sum of the ordering and holding costs per gallon will be $707.
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