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# Sample Solution: Linear optimization: Inventory Management

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Sales per year 10,400 cd's

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

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!