Problem $19-13($Algo$)$

Shoney Video Concepts produces a line of video streaming servers that are linked to personal computers for storing movies. These

devices have very fast access and large storage capacity.

Shoney is trying to determine a production plan for the next $12$ months. The main criterion for this plan is that the employment level is

to be held constant over the period. Shoney is continuing in its R&D efforts to develop new applications and prefers not to cause any

adverse feelings with the local workforce. For the same reason, all employees should put in full workweeks, even if that is not the

lowest$-$cost alternative. The forecast for the next $12$ months is

Manufacturing cost is $$200$ per server, equally divided between materials and labor. Inventory storage cost is $$4$ per unit per month

and is assigned based on the ending inventory level. A shortage of servers results in lost sales and is estimated to cost an overall $$24$

per unit short.

The inventory on hand at the beginning of the planning period is $200$ units. Eight labor hours are required per DVD player. The

workday is seven hours.

Develop an aggregate production schedule for the year using a constant workforce. For simplicity, assume $22$ working days each

month except July, when the plant closes down for three weeks' vacation $($leaving seven working days$).$ Assume that total annual

production capacity is greater than or equal to total annual demand $($i$.$e$.,$ compute workforce level based on annual demand and

annual capacity$).$

Note: Leave no cells blank $-$ be certain to enter $"$O$"$ wherever required. Indicate monthly shortages using a negative ending

inventory level. Round up the "number of workers" to the next whole number and round down your monthly "Available

production" values to the nearest whole number.