Question

A manufacturer of exercise equipment purchases the pulley section of the equipment from a supplier who lists these prices: $5 each for less than 1,000; $4.95 each for 1,000 to 3,999; $ 4.90 each for 4,000 to 5,999; and $4.85 for 6,000 or more. Fixed ordering costs are $50.00, annual holding costs are 40 percent of the purchase cost, and annual demand is 4,900 pulleys. Determine an order quantity that will minimize total cost.

Answer 1

Answer:

500 units

Explanation:

An order quantity that will minimize total cost is the economic order quantity (EOQ). In order to calculate this, we use the EOQ formula as follows:

$EOQ = \sqrt{\frac{2DF}{H} }$ ............................................................. (1)

D = Demand or annual usage = 4,900

F = Fixed ordering cost = $50

H = Holding cost = 40% × $4.90 = $1.96

Note that since annual demand is 4,900 which falls within 4,000 to 5,999, the purchase cost is therefore $4.90.

Substituting the values into equation (1), we have:

$EOQ = \sqrt{\frac{2*4,900*50}{1.96} } = \sqrt{\frac{490,000}{1.96} } = \sqrt{250,000} = 500$

Therefore, an order quantity that will minimize total cost is 500 units.

Answer 2

Answer: The quantity that will minimize total cost is 500 units.

Explanation: To solve this, we will be using a mode called Economic Order Quantity.

Economic Order Quantity (EOQ) is the total number of units that a company has to add to inventory with each order to minimize the total costs of inventory, such as holding costs, order costs, and shortage costs.

Therefore, the EOQ model finds the quantity that minimizes the sum of these costs.

The formula for calculating EOQ is given as:

EOQ = √2DF/H

Where;

D = Demand or annual usage = 4,900

F = Fixed ordering cost = $50

H = Holding cost = 40% × $4.90 = $1.96

From the question above, we can conclude that since annual demand is 4,900 which falls within 4,000 to 5,999, then the purchase cost is therefore $4.90.

Now, we will substitute these values into the equation above, thus:

EOQ = √2 x 4,900 x 50/1.96

EOQ = √490,000/1.96

EOQ = √250,000

EOQ = 500

Therefore, the quantity that will minimize total cost is 500 units.