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# ABX manufactures large freezers for grocery stores. ABX is presently trying to plan its production

Question: ABX manufactures large freezers for grocery stores. ABX is presently trying to plan its production and inventory levels for the next six months. Because of seasonal ﬂuctuations in utility and raw materials costs, the per unit cost of producing freezers varies from month to month–as does the demand for the products. Production capacity also varies from monthABX manufactures large freezers for grocery stores. ABX is presently trying to plan its production and inventory levels for the next six months. Because of seasonal ﬂuctuations in utility and raw materials costs, the per unit cost of producing freezers varies from month to month–as does the demand for the products. Production capacity also varies from month to month due to diﬀerences in the number of working days, vacations, and scheduled maintenance and training. The following table summarizes the monthly production costs, demands, and production capacity that ABX’s management expects to face over the next 6 months.

Month
1
2
3
4
5
6
Unit Production Cost
\$225
\$250
\$230
\$275
\$290
\$260
Unit Demanded
1,200
3,000
5,000
5,500
3,500
3,600
Maximum Production
4,000
3,200
3,800
6,000
4,000
3,000
The warehouse can hold a maximum of 5,500 units in inventory at the end of each month. Management wants to keep at least 1,500 units in inventory as safety stock to balance variations in demand. To maintain stable workforce, the company wants to produce no less than one half of its maximum production capacity each month. The accounting department estimates that the cost of carrying a unit in any month is approximately equal to 1.5% of the unit production cost in the same month. ABX estimates the number of units carried in inventory each month by averaging the beginning and ending inventory for each month.
There are 3,600 units currently in inventory. ABX wants to identify the production and inventory plan for the next six months that will meet the expected demand each month while minimizing production and inventory costs.

What is the best total production and inventory cost? (Do not include dollar sign)

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