The ABC Bumper Inc. manufactures bumpers for automobiles for one of the big thre
ID: 363249 • Letter: T
Question
The ABC Bumper Inc. manufactures bumpers for automobiles for one of the big three auto companies. About 60,000 pairs of bumpers (front bumper and rear bumper) are ordered by the auto company per year, at a price of $150.00 per pair. Pairs of bumpers are produced at a rate of about 400 per working day, and the company operates 240 days per year. The company manufactures other products, and it must set up the manufacturing system for a production order for pairs of bumpers, which costs $250.00. It costs $2.50 to store one pair of bumpers for one month.
a. What is the EOQ?
b. What is the annual carrying cost?
c. What is the annual setup cost?
d. What is the annual total cost?
e. What is the total annual expense of producing the EOQ every time?
f. How many production runs will be required per year?
g. What is the total annual expense of manufacturing 3,000 pairs of bumpers per production run? How much is saved per year by producing the EOQ every time?
Explanation / Answer
Variables
P (purchase unit price)= $150.00 per pair
Q (order quantity)= 60,000 Pairs
Q (optimal order quantity) = 250
D(annual demand quantity) = 400 pair per working day*240 days(company operates)= 96000
K (fixed cost per order i.e. cost of ordering and shipping and handling)= 250$
h (annual holding cost per unit)= $2.50 one pair then price per year = 2.50$*12 = 30$
Now let us see the Total Cost function & EOQ formula
The single-item EOQ formula finds the minimum point of the following cost function:
Total Cost = purchase cost + ordering cost + holding cost
Where:
Purchase cost: This is the variable cost of goods: purchase unit price (150$) × annual demand quantity (60,000). This is P × D = 150$ x 60,000 = 9000000$
Ordering cost: This is the cost of placing orders: each order has a fixed cost K, and we need to order D/Q times per year. This is K(250$) × D(60000)/Q(250) = 60000$
Holding cost: the average quantity in stock (between fully replenished and empty) is Q/2, so this cost is h (30) × Q (60000$)/2 = 900000$
Now let us derive total cost by the following formula:
Total Cost = purchase cost + ordering cost + holding cost
So
Total Cost= 9000000$ + 60000$ + 900000$
Total Cost= 9960000$
a. What is the EOQ?
Answer:
EOQ = Number of pairs ordered 60000 / 240 days company operates
EOQ= 250 Pairs
b. What is the annual carrying cost?
Annual carrying cost = Total pair produced in a year (400pair*240 days= 96000) - Order quntity i.e. 60000* holding cost per year i.e. 30$
Annual carrying cost = 96000-60000*30
Annual carrying cost = 36000*30
Annual carrying cost = 1080000 $
c. What is the annual setup cost?
Annual setup cost= total qty produced (96000)*unit price (250$)* holding cost yearly(30$)
Annual setup cost= 720000000 $
d. What is the annual total cost?
otal Cost = purchase cost + ordering cost + holding cost
So
Total Cost= 9000000$ + 60000$ + 900000$
Total Cost= 9960000$
e. What is the total annual expense of producing the EOQ every time?
Total annual expense= EOQ per day (250 pairs)*total working days in year (240)* Ordering cost (150$)
Total annual expense= 9000000 $
f. How many production runs will be required per year?
production runs required per year = total working days in year (240)
production runs required per year = 240
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