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 $4.75 per kg. Sarah’s annual holding cost of one kg of palm oil is 25% of the purchase price. Sarah wants to minimize her annual fixed ordering and inventory holding costs, i.e., the EOQ cost per year C(Q).
A) Model Inputs:
Fixed ordering cost K =$ ________
Unit holding cost h =$ _________ per kg per year. (Keep two decimals in your answer)(0.2 points)
Annual demand rate R = _________ kgs per year. (0.2 points)
B) How much palm oil should Sarah purchase with each order (in kgs), i.e., what is the value of the economic order quantity (EOQ)?
EOQ: Q*= __________ kgs. (Round your answer to the nearest integer.)
Please show detailed analysis below:
C) The EOQ cost per year associated with Q*: C(Q*) = $ ____________
Please show detailed analysis below: (Keep one decimal in your answer):
D) Sarah needs to place a new order of palm oil every ______ days. (1 year = 260 days.) (0.25 points)
Please show detailed analysis below: (Keep two decimal in your answer):
E) 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:
F) 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