. Sarah’s Organic Soap Company makes four kinds of organic liquid soap- “regular
ID: 2479957 • Letter: #
Question
. Sarah’s Organic Soap Company makes four kinds of organic liquid soap- “regular”, “lavender”, “citrus” and “tea tree”. Demand for the four scents are 150, 120, 75 and 50 kgs per hour respectively. Sarah’s production process can produce any soap at the rate of 450 kgs per hour but 1.5 hours are needed to switch between scents. During those switchover times, the process doesn’t produce any soap. Sarah wants to choose a production schedule that (i) cycles repeatedly through the four scents, (ii) meets the required demand and (iii) minimizes the amount of inventory held.
A? How many kgs of “regular” should Sarah produce before switching over to another scent? (Hint: the Process Capacity = Demand)
b? Sarah needs to purchase organic Palm Oil to make the soaps. She needs 1,000 kgs of palm oil per day on average. The supplier charges a $60 delivery fee per order (independent of the order size)and $4.75 per kg. Sarah’s annual holding cost equals 25%. Assume 52 weeks per year and 5 days per week. If Sarah wants to minimize inventory holding and ordering costs, how much palm oil should she purchase with each order (in kgs)? (Hint: use the EOQ formula)
Explanation / Answer
A)
We will take following assumptions as per details given
Within a production cycle, Sarah produces all four types of soaps with total setup time = 1.5 x 4 = 6 hours
Total demand for all four scents of soaps per hour = 150+120+75+50 =395 kgs/hour
With the optimal batch size of B, The process capacity should equal the demand, which is 395 kgs/hr, which gives the following equation.
B / (6 + 1/450 x B) = 395 kgs/hour
B =(395 * 6) / (1- 395/450)= 19390.91 kgs.
Note that the proportion of regular soap among all soaps is 150/395.
Therefore, in each batch, 150/395*19390.91 =7363.636kgs of "regular" should be produced.
B) we will have to calculate the economic order quantity of purchase of palm oil , in which the inventory and ordering cost are minimized
the formula of EOQ is given below
EOQ=sqrt(2KR/h)
Where
K = $60
R = 1000 kg per day
H = holding cost which is = $4.75/kg x 0.25/year / (52 weeks/year x 5 days/week) = $0.004567/day
Putting the values in the formula
EOQ=sqrt(2KR/h)
EOQ = sqrt(2$60*1000/($4.75*0.25/(525)))
EOQ= 5125.786 kgs.
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