PROBLEM $(25$ POINTS$)$

A local manufacturing company with facilities in Arecibo produces toys for children. The projected demand for one of the most popular toys, Super Robocop, is shown in the following table for the first quarter of the year:

Assume a regular eight$-$hour workday. Suppose the regular time of an employee costs $$12\mathrm{.}50$ per hour.

The hiring costs are $$350$ per worker, and the firing costs, including severance pay, are $$850$ per worker. The cost of holding inventory is $$4\mathrm{.}00$ per unit added per month. Assume it takes on average one hour and $40$ minutes for a worker to assemble a toy robot. Shortages are not allowed. Assume that the inventory at the end of December of the previous year was $600$ units of these toys, and that management wants to maintain an inventory of $800$ units at the end of April.

Assume that at the end of December of the previous year, they had a workforce of $35$ workers. Note: For modeling$/$computations purposes, use adjusted demand.

Formulate this problem as a linear programming model. Define all variables and include all necessary constraints. You must provide examples of the main computations you made to work with your model, such as conversion factors.

As a BONUS $(10$ points$),$ solve the linear programming model using Excel or the program of your choice $($Lingo$,$ Maple, etc.$).$ Compare the cost analysis obtained with this model versus one based on the chase strategy. Upload the file of your original work with the corresponding analysis including comments.