Question

# Sarah’s Organic Soap Company makes organic liquid soap. One of the raw materials for her soaps...

Sarah’s Organic Soap Company makes organic liquid soap. One of the raw materials for her soaps is organic palm oil. She needs 500 kgs of palm oil per day on average. The supplier charges a \$55 delivery fee per order (which is independent of the order size) and \$5.5 per kg. Sarah’s annual holding cost is 15%. Assume she operates and sells 5 days per week, 52 weeks per year.

a.If Sarah wants to minimize her annual ordering and inventory holding costs, how much palm oil should she purchase with each order (in kgs)?kgs(Round to nearest integer.)

b.If Sarah orders 4250 kgs with each order, what would be the annual sum of ordering and holding costs? (Round your answer to 3 decimal places.)

c.If Sarah orders 8100 kgs with each order, what would be sum of ordering and holding costs per kg sold? per kg

d.Sarah’s supplier is willing to sell her palm oil at a 5% discount if she purchases 15,000 kgs at a time. If she were to purchase 15,000 kgs per order what would be her annual sum of ordering and holding costs?

a) to minimize holding and ordering cost we need to find the optimal order quantity EOQ.

EOQ = (2*D*O/h)

D = annual demand = daily demand*days*weeks = 500*5*52 = 130000

O = order cost = 55

h = holding cost = 15% of per kg cost = 15%*5.5 = 0.825

EOQ = (2*130000*55/0.825) = 17333333.3 = 4163.33 kg = 4163 kg in each order

b) order quantity (Q) = 4250

total cost = ordering + holding cost

= D*O/Q + Q*h/2

= 130000*55/4250 + 4250*0.825/2

= 1682.353 + 1753.125

= 3435.478

c) Q = 8100

total cost = ordering + holding cost

= D*O/Q + Q*h/2

= 130000*55/8100 + 8100*0.825/2

= 882.716 + 3341.25

= 4223.966

d) Q = 15000

total cost = ordering + holding cost

= D*O/Q + Q*h/2

= 130000*55/15000 + 15000*0.825/2

= 476.667 + 6187.5

= 6664.167

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