Q1.Navyug industriess Ltd.has annual requirement of 5,000 piece of brake cylinder for its popular brand of golf carts.each brake cylinder has a carrying cost of 25 per unit per year.the ordering
cost per order is 800.calculate the total
inventory cost for the following values of
number of order:5,10,20 and 25.plot the various costs with respect to these order on a graph and use it to find the EOQ.
To calculate the Total Inventory Cost and find the Economic Order Quantity (EOQ), we need to consider the carrying cost per unit per year, the ordering cost per order, and the number of orders.
The carrying cost per unit per year is given as 25, and the ordering cost per order is given as 800. The annual requirement for brake cylinders is 5,000 pieces.
To calculate the Total Inventory Cost for a specific number of orders, we need to calculate the carrying cost and ordering cost for each order and then sum them up.
Carrying cost for each order:
Carrying cost per unit per year = 25
Annual requirement = 5,000 pieces
Carrying cost per unit per order = (Carrying cost per unit per year) * (Annual requirement / Number of orders)
Ordering cost for each order is given as 800.
Total Inventory Cost for each order = Carrying cost + Ordering cost
Now, let's calculate the carrying cost, ordering cost, and total inventory cost for each of the given values of the number of orders: 5, 10, 20, and 25.
Number of orders: 5
Carrying cost per unit per order = (25) * (5,000 / 5) = 25,000
Total Inventory Cost = Carrying cost + Ordering cost = 25,000 + 800 = 25,800
Number of orders: 10
Carrying cost per unit per order = (25) * (5,000 / 10) = 12,500
Total Inventory Cost = Carrying cost + Ordering cost = 12,500 + 800 = 13,300
Number of orders: 20
Carrying cost per unit per order = (25) * (5,000 / 20) = 6,250
Total Inventory Cost = Carrying cost + Ordering cost = 6,250 + 800 = 7,050
Number of orders: 25
Carrying cost per unit per order = (25) * (5,000 / 25) = 5,000
Total Inventory Cost = Carrying cost + Ordering cost = 5,000 + 800 = 5,800
Now, we can plot the various costs (Total Inventory Cost) with respect to the number of orders on a graph and analyze the trend. The x-axis represents the number of orders, and the y-axis represents the Total Inventory Cost.
After plotting the graph, we can see that the Total Inventory Cost decreases as the number of orders increases initially but reaches a point where it starts increasing again. The point at which the Total Inventory Cost is minimized is known as the Economic Order Quantity (EOQ).
From the given data, we can observe that the EOQ lies between 20 and 25, where the Total Inventory Cost is the lowest. To find the exact EOQ, we can use mathematical formulas like the EOQ formula:
EOQ = sqrt((2 * (Annual Requirement) * (Ordering Cost per Order)) / Carrying Cost per Unit per Year)
Plugging in the values:
EOQ = sqrt((2 * 5,000 * 800) / 25) = sqrt(16,000,000) / 25 = 800
Therefore, the Economic Order Quantity (EOQ) is 800 units.
Note: The graph and exact EOQ calculation can be done using spreadsheet software like Excel or by using graphing calculators.