Answer :
Optimal number of detectors to be ordered on each order if purchased at the price of discount. The optimal number of detectors to be ordered on each order is 7 units.
Given, Annual demand of a metal detector for the airport = 1650 units.
Cost of a detector for Wang = $445.
Cost of storage is 20% of the unit cost.
Cost of placing each order = $25.
Cost of a detector for order of 300 or more = $371.
The supplier takes 6 days to deliver it.
Number of business days in a year = 250.1) Optimal number of detectors to be ordered on each order if bought at price regular.
Total units required per year = 1650 units
Cost of ordering 1 unit at a time = 1650 × ($445 + 0.2 × $445)/300 + $25 = $837.50
Cost of ordering 2 units at a time = 825 × ($445 + 0.2 × $445)/600 + $25 = $663.75
Cost of ordering 3 units at a time = 550 × ($445 + 0.2 × $445)/900 + $25 = $597.78
Cost of ordering 4 units at a time = 413 × ($445 + 0.2 × $445)/1200 + $25 = $560.04
Cost of ordering 5 units at a time = 330 × ($445 + 0.2 × $445)/1500 + $25 = $536.25
Cost of ordering 6 units at a time = 275 × ($445 + 0.2 × $445)/1800 + $25 = $520.83
Cost of ordering 7 units at a time = 236 × ($445 + 0.2 × $445)/2100 + $25 = $510.71
Cost of ordering 8 units at a time = 206 × ($445 + 0.2 × $445)/2400 + $25 = $503.13
Therefore, the optimal number of detectors to be ordered on each order if bought at the price regular is 7 units. The optimal number of units that should be ordered on each order when purchased at a discounted price is the same as when purchased at the regular price because the cost of ordering, storage, and number of days required for delivery do not change.
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1. The EOQ model finds Roger Dist.'s optimal order size is approximately 30 units at the regular price, 2. About 33 units should be purchased at the discounted price, 3. The annual adjusting amount is $137.50.
Optimal Order Quantity for Metal Detectors
To determine the optimal number of metal detectors Roger Dist. should order, we'll use the Economic Order Quantity (EOQ) model. The formula for EOQ is:
[tex]EOQ = \sqrt{\frac{2DS}{H}}[/tex]
where D is the annual demand, S is the cost per order, and H is the holding cost per unit per year.
1. Regular Price
- Annual Demand (D): 1650 units
- Cost per Order (S): $25
- Holding Cost per Unit per Year (H): 20% of $445 = $89
Plugging these values into the EOQ formula:
[tex]EOQ = \sqrt{(2 * 1650 * 25) / 89} = 30 units[/tex]
2. Discounted Price
- Annual Demand (D): 1650 units
- Cost per Order (S): $25
- Holding Cost per Unit per Year (H): 20% of $371 = $74.20
Plugging these values into the EOQ formula:
[tex]EOQ = \sqrt{(2 * 1650 * 25) / 74.20} = 33 units[/tex]
3. Adjusted Amount for Regular Price
Since the supplier offers a discount for orders of 300 or more, let's determine the total cost for the adjusted amount:
Ordering Quantity: 300 units
Annual Holding Cost: (300/2) × $89 = $13,350
Annual Ordering Cost: (1650/300) × $25 = $137.50
Since the total cost might be higher or lower depending on the realistic batch sizes, a deeper cost benefit analysis is recommended.
