Answer:
Step-by-step explanation:
1. To compute the average annual ordering and carrying cost, we need to first determine the number of orders that the company places in a year. Assuming that the company operates for 12 months in a year, we can calculate the number of orders as follows:
Number of orders = Annual demand / Order quantity
Order quantity = Production volume = 450 cars
Annual demand = Production volume x Number of months = 450 x 12 = 5400 cars
Number of orders = 5400 / 450 = 12 orders per year
The annual ordering cost can be calculated by multiplying the number of orders by the cost per order:
Annual ordering cost = Number of orders x Cost per order = 12 x TZS
To compute the annual carrying cost, we need to determine the average inventory. The average inventory can be calculated as:
Average inventory = Order quantity / 2 = 450 / 2 = 225 cars
To compute the annual carrying cost, we need to determine the average inventory. The average inventory can be calculated as:
Average inventory = Order quantity / 2 = 450 / 2 = 225 cars
The annual carrying cost can be calculated as:
Annual carrying cost = Average inventory x Cost per unit x Carrying cost percentage
Cost per unit = Cost of engine = TZS20
Carrying cost percentage = 15% = 0.15
Annual carrying cost = 225 x TZS20 x 0.15 = TZS675
Therefore, the average annual ordering and carrying cost is:
Average annual ordering and carrying cost = Annual ordering cost + Annual carrying cost = TZS + TZ
2. To compute the average inventory, we can use the following formula:
Average inventory = (Q/2) + (D*LT)/2
where Q is the order quantity, D is the annual demand, and LT is the lead time for the engines.
We first need to calculate the annual demand for engines. Since the company produces 450 cars in one month, and each car requires one engine, the monthly demand for engines is 450. Therefore, the annual demand for engines is:
Annual demand = Monthly demand * 12 = 450 * 12 = 5400 engines per year
Next, we need to determine the order quantity that minimizes the total cost of ordering and carrying inventory. We can use the economic order quantity (EOQ) formula
EOQ = sqrt((2 * D * S) / H)
where S is the ordering cost and H is the carrying cost as a percentage of the unit cost.
The ordering cost is given as TZS per order, so S = TZS. The carrying cost is 15% of the unit cost of TZS20 per engine, so H = 0.15 * 20 = TZS3.
Plugging in the values, we get:
EOQ = sqrt((2 * 5400 * TZS) / TZS3) = sqrt(36000) = 189.74
Therefore, the order quantity that minimizes the total cost of ordering and carrying inventory is 190 engines per order.
Finally, we can use the formula for average inventory to compute the average inventory:
Average inventory = (Q/2) + (DLT)/2
= (190/2) + (5400/12)(1/2) = 95 + 225 = 320 engines
Therefore, the average inventory for the car manufacturing company is 320 engines.