Problem 1 SECOND REQUEST ANSWER ONLY BONUS QUESTION. THIS WAS ANSWERED SEE BELOW
ID: 2467712 • Letter: P
Question
Problem 1 SECOND REQUEST ANSWER ONLY BONUS QUESTION. THIS WAS ANSWERED SEE BELOW. NEED BONUS QUESTION ANSWERED
Chapter 9: A specialty coffeehouse sells Colombian coffee at a fairly steady rate of 65 pounds per week. The beans are purchased from a local supplier for $4 per pound. The coffeehouse estimates that it costs $50 in paperwork and labor to place an order for the coffee, and the annual holding cost is 20% of the purchasing price. (Use 52 weeks/year)
What is the economic order quantity (EOQ) for Colombian coffee?
What is the optimal number of orders per year?
What is the optimal interval (in weeks) between the orders?
(BONUS – 5 points) Assume that the coffeehouse’s current order policy is to buy the beans every 13 weeks. The manager says that the ordering cost of S = $50 is only a guess. Therefore, he insists on using the current policy. Find the range of S for which the EOQ you found in part a) would be preferable (in terms of a lower total replenishment and carrying costs) to the current policy of buying beans every 13 weeks.
a. Economic Order Quantity is the optimal order size to minimize all inventory costs. The formula is written as
EOQ = [2FD/C]^1/2
Where C=Carrying cost per unit per year = In our problem the carrying cost is 20%of the purchasing price
which is 0.20(65 units*$4*52) = 2704
F=Fixed cost per order which is $50 for paperwork and others
D=Demand in units per year is 65*52 =3380
Solving the above formula = ((2*50*3380)/2704)^(1/2) = (125)^(1/2) = 11.18
(b) Optimal number of orders per year
Optimal order quantity (Q*) is found when annual holding cost = ordering cost
solving for the above equation = Sqrt ((2*3380*50)/0.8) =650
holding cost per unit per year = 0.2*4 =0.8
What is the optimal interval (in weeks) between the orders?
T* = Q* /D = 650 /3380 = 0.1923 yrs
Assuming 52 weeks
Explanation / Answer
Your EOQ calculation is not correct,Correct Calculation is :
EOQ = (2FD/C)^(1/2)
= [( 2 * 3,380 * 50 ) / 0.80] ^ (1/2)
= 650 Units
C = Carrying cost per unit = 20% of Purchase price = 20% of $ 4 = 0.80
b) optimal orders per year
= Annual Quantity required / EOQ
= 3,380 / 650
= 5.2 Orders
c) Optimal Interval between Orders
= No. of weeks / Optimal no. of orders
= 52 / 5.2
= 10 Weeks
Bonus Part
Total Cost as per Current policy
Purchase cost = Demand X Purchase price = 3,380 X $ 4 = 13,520
Carrying Cost = 20% of Purchase cost = (845/2) X ( 20% X 0.8 ) = 338
Ordering Cost = No. of orders X Fixed Cost = 4 X $ 50 = $ 200
Total Cost = 14,058
So range of S falls where the total Cost would not exceed 14,058
Purchase cost + Carrying Cost + S X Ordering Quantity = 14,058
13,520 + ( 650 / 2 ) X 0.8 + S X 5.2 = 14,058
13,780 + 5.2 S = 14,058
5.2S = 14,058 - 13,780
S = 278 / 5.2
S = $ 53.46
So the range of S lies from 50 to 53.46 so that it will be preferred over Current policy.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.