The owners of Oceania Electronics are planning their buying policy for a 3-month period. They buy gadgets in lot sizes of 200, 400, 600, 800 and 1000. However, quantity discounts apply, so that

200 costs $4 000,

400 costs $5 500,

600 costs $6 800,

800 costs $8 000, and

1 000 costs $8 500.

Anticipated demand over the 3-month period is as follows:

Month 1 2 3

demand 600 1000 800

An inventory holding charge of seven dollars per item is incurred per month based on the end-ofmonth inventory including month 3. Shortages are also allowed but are limited to 200 per month and are charged at ten dollars per item based on the end-of-month inventory which also includes month 3.

The companys storage space will only handle 1000 items at a time. There is 800 of storage at the start of the planning period, and the gadget sold in the month of purchase need not be stored.

Determine the how many items should be ordered each month to minimize the total cost of buying and storing of gadgets to meet the anticipated demand of gadgets by using dynamic programming.