Frigo Inc manufactures refrigerators for grocery stores. Frigo Inc is presently trying to plan its production and inventory levels for the next six months. Because of seasonal $$uctuations in utility and raw materials costs, the per unit cost of producing freezers varies from month to month$$as does the demand for the products. Production capacity also varies from month to month due to di$$erences 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 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

$1,200$

$4500$

$5,000$

$5,500$

$3,500$

$3,600$

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 $2\%$ of the unit production cost in the same month. Frigo Inc 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. Frigo Inc wants to identify the production and inventory plan for the next six months that will meet the expected demand each month while minimizing total cost.

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