Sample Solution: Linear optimization: Inventory Management
Sales per year 10,400 cd's
Mfg/Purchasing Costs
She buys from supplier >= 1000 at $4.45 ea CD
She buys from supplier <=1000 at $4.50 ea CD
Delivery Charge from her supplier is $10/shipment regardless of size
She pays Finance Rate annual interest rate 15%
She pays NYS Property Tax 5% on Annual Inv Value
She pays Insurance Charges 0.02 for every dollar of inventory
She Buys from her supplier 200 CD's/Week
How much does inv management cost her?
Best small order inventory plan?
how big are her orders?
how much does it cost her?
How much does she save?
https://brainmass.com/math/optimization/sample-solution-linear-optimization-inventory-management-590717
SOLUTION This solution is FREE courtesy of BrainMass!
Sales per year 10,400
Quantity Price per unit
Less than 1,000 $4.45
More than 1,000 $4.50
Delivery charge per shipment $10
Finance rate 15%
Property tax 5% of invetory value
Insurance charges 0.02 for every dollar of inventory
Order size 200
Number of orders per year = (Sales per year/Order size) 52
Average inventory 200
Delivery charge per year = Number of orders per year*Delviery charge per shipment $520.00
Finance cost = Average inventory*Price per unit*Finance rate $133.50
Property tax = Average inventory*Price per unit*Property tax $44.50
Insurance charges = Average inventory*Price per unit*Insurance charges $17.80
Total cost $715.80
Order size 326.00
Number of orders per year = (Sales per year/Order size) 31.90184049
Average inventory 326
Delivery charge per year = Number of orders per year*Delviery charge per shipment $319.02
Finance cost = Average inventory*Price per unit*Finance rate $217.61
Property tax = Average inventory*Price per unit*Property tax $72.54
Insurance charges = Average inventory*Price per unit*Insurance charges $29.01
Total cost $638.17
Savings $77.63
She has to order 326 units every time
https://brainmass.com/math/optimization/sample-solution-linear-optimization-inventory-management-590717