Sarah’s Organic Soap Company makes organic liquid soap. One of the raw materials
ID: 344540 • Letter: S
Question
Sarah’s Organic Soap Company makes organic liquid soap. One of the raw materials for her soaps is organic palm oil. She needs 1,000 kgs of palm oil per day on average, i.e., the demand rate of palm oil is 1,000 kgs per day. Assume she operates and sells 5 days per week, 52 weeks per year, i.e., 1 year = 260 days (5 days/week * 52 weeks/year = 260 days/year). The supplier charges a $60 delivery fee per order (which is independent of the order size). The purchase price of the palm oil is $4.75 per kg. Sarah’s annual holding cost of one kg of palm oil is 25% of the purchase price. Sarah wants to minimize her annual fixed ordering and inventory holding costs, i.e., the EOQ cost per year C(Q).
If the palm oil can only be purchased as batches with a batch size of 500 kgs, then how much palm oil should Sarah order instead?
Sarah needs to order ____________ kgs of palm oil every time. (0.6 points)
Please show detailed analysis below:
If the demand rate increases from 1,000 kgs per day to 3,000 kgs per day, the EOQ will (0.4 points)
Remain the same
Increase three times
Increase more than three times
Increase, but less than three times
Cannot be determined
Explanation / Answer
EOQ = square root ( 2* Annual Demand * Odering cost / Per Unit annual holding cost)
Daily demand = 1000
Annual Demand = 260* 1000 = 260,000
Ordering cost = 60 per order
purchase price = 4.75
Holding cost = .25 * 4.75 = 1.1875
EOQ = squareroot (2*260,000 *60/1.1875) = 5125
Since Sarah can only order in multiples of 500, we need to calculate total inventory prices at 5000 and 5500
Total cost = Carrying cost + Ordering cost
= per unit holding cost * average inventory + Per order cost * number of order
At Q= 5000
Total cost = 1.1875 * (5000/2) + 60 *(260000/5000) = $6088
At Q = 5500.
Total cost = 1.1875 * (5500/2) + 60 *(260000/5500) = $6101
Hence Sarah's order size should be 5000 KG for minimum total inventory cost
-----------------------------------------
When demand rate increases to 3000 Kg per day
EOQ = squareroot (2*780,000 *60/1.1875) = 8878
Since she can order in quants of 500, we need to check at 8500 and 9000
At Q= 8500
Total cost = 1.1875 * (8500/2) + 60 *(780,000/8500) = $10552
At Q = 9000.
Total cost = 1.1875 * (9000/2) + 60 *(780000/9000) = $10543
Hence the Sarah should order 8500 units each time
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