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Problem $13-7($Algo$)$

Trexoid Incorporated makes a popular video game console. Demand varies each month, with highest demand coming in the last quarter of the year. Regular production costs are $\backslash (\backslash$$ $340\backslash )$ per unit and inventory carrying cost is $\backslash (\backslash$$ $2\backslash )$ per unit per quarter. Overtime production cost is $\backslash (\backslash$$ $370\backslash )$ per unit. Assume that the $25$ current Trexoid employees can produce a total of $50,000$ units per quarter in regular production and can work enough overtime hours to produce the amount required if a chase plan is employed. On the other hand, hiring cost is $\backslash (\backslash$$ $5,000\backslash )$ per employee and firing cost is $\backslash (\backslash$$ $12,500\backslash )$ per employee. Trexoid currently has zero inventory on hand, and it would like to have zero inventories at the end of the year. Assume that hiring and layoff$/$firing$,$ if necessary, occur at the beginning of the quarter. Forecast demand is as follows:

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a$.$ Given the above demand estimate, develop a production plan based on level production.

b$.$ Determine the cost of the level production plan.

c$.$ Given the planning information, develop a production plan based on chase production.

d$.$ Determine the cost of the chase production plan.

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Required C