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There are 2 steps to solve this one.
3/6
Answer:- According to given data
A) Demand (D) = 400× 12 months = 4800
Order cost = $120
Holding cost = $35
EOQ = Sqrt(2×D×S)/H = sqrt(2×4800×$120/$35) = 181 units
Which falls in 100-199
Total cost = Holding + Ordering + Purchase price
= (Q/2)×H + (D/Q)×S + P×D
= (181/2)×$35 + (4800/181)×$120 + 4800×$325
= 3,174.901573277+3,174.901573284+1,560,000
= $1,566,350
For EOQ = 200
Total cost = (200/2)×$35 + (4800/200)×$120 + 4800×$300
= 3,500+2,880+1,440,000
= $1,446,380
So the optimal order quantity is 200 units with total cost $1,446,380 Explanationfor step 1
Inventory cost is nothing but the holding cost and ordering cost and purchase cost.
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B) If the holding cost is 10% of price
EOQ = sqrt(2×4800×$120/($350×0.10)) = 181 units
Total cost = (181/2)×$35 + (4800/181)×$120 + 4800×$350
= 3,174.901573277+3,174.901573284+1,680,000
= $1,686,350
EOQ = sqrt(2×4800×$120/$32.5) = 188 units
Total cost = (188/2)×$32.5 + (4800/188)×$120 + 4800×$325
= 3,059.411708158+3,059.41170816+156,000
= $1,621,190
EOQ = sqrt(2×4800×120/30) = 196 units -- Not feasible
EOQ = 200
Total cost = (200/2)×$30 + (4800/200)×$120 + 4800×$300
= 3,000+2,880+1,440,000
= $1,445,880
From the above analysis the best optimal order quantity is EOQ = 200 with cost of $1445880
Explanationfor step 2
Here also the best optimal order is 200 units because of all the low inventory costs
(a). What is the optimal order quantity and what is the optimal cost? --- 200 units with $1446380
(b). What is the optimal order quantity if 10% is used instead of $35 and what is the optimal cost? --- 200 units with $1445880
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