Decorum, Inc., manufactures high-end ceiling fans. Their sales are seasonal with higher demand in the warmer summer months. Typically, sales average 400 units per month. However, in the hot summer months (June, July, and August), sales spike up to 600 units per month. Decorum can produce up to 500 units per month at a cost of $300 each. Decorum sells the ceiling fans for $500 each. Decorum can carry inventory from one month to the next, but at a cost of $20 per ceiling fan per month. Decorum has 25 units in inventory at the start of January.

The decision to be made is the total amount of fans to produce with the objective of our optimization model to maximize total profit.

Suppose Decorum makes 450 ceiling fans in January and 500 in February. Calculate by hand the following costs. (Note that holding costs are charge for the fans left in inventory at the end of the month. For instance, if Decorum has 25 fans at the beginning of a month, it makes 450 fans in that month, and it sells 400 fans in that same month, then there are 75 fans left at the end of the month, for which it needs to charge $20 per fan for holding cost. The 75 fans become the beginning inventory for the next month.)

Assuming Decorum must produce enough ceiling fans to meet demand, how many ceiling fans should Decorum produce each month over the course of the next year (i.e., January to December) to optimize its objective?

Make a rough sketch of a spreadsheet model, with blocks laid out for the data cells, changing cells, output cells, and objective cell. Build a spreadsheet model for January and February and thoroughly test the model. Build and solve a linear programming spreadsheet model for the full problem (i.e., January to December).

Beginning inventory: 75 units (from January)

Produced: 500 units

Sold: 400 units

Remaining inventory: 175 units Holding Cost = 175 units * $20 per unit = $3,500

What is the value of the objective function for the optimal solution?

(please don't just describe how to do it in excel, please do it in excel and provide an answer of the value of the objective function for the optimal solution with steps of how it was done in excel)