EZ Windows, Inc manufacturers replacement windows for the home remodelingbusiness In January, the company produces 15,000 windows and ended the monthwith9,000windowsininventory EZ Windows'managementteamwouldliketode velop a production schedule for the next three moths A smooth production scheduleis obviously desirable because it maintains the current workforce and provides a sim ilar month to month operation However, given the sales forecasts, the productioncapacities, and the storage capabilities as shown in Table 2, the management teamdoes not think a smooth production schedule with the same production quantity eachmonthpossible The company's cost accounting department estimates that increasing productionbyonewindowfromonemonthtothenextwillincreasetotalcostsby$1 00foreach Table2 Problem1 8 February March April Salesforecast 15,000 16,500 20,000 Productioncapacity 14,000 14,000 18,000 Storagecapacity 6,000 6,000 6,000 unit increase in the production level In addition, decreasing production by one unitfrom one month to the next will increase total costs by $0 65 for each unit decrease inthe production level Ignoring production and inventory carrying costs, formulate alinear programming model that will minimize the cost of changing production levelswhilestillsatisfyingthemonthlysalesforecasts

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EZ-Windows, Inc. manufacturers replacement windows for the home remodelingbusiness. In January, the company produces 15,000 windows and ended the monthwith9,000windowsininventory.EZ-Windows'managementteamwouldliketode-velop a production schedule for the

EZ-Windows, Inc. manufacturers replacement windows for the home remodelingbusiness. In January, the company produces 15,000 windows and ended the monthwith9,000windowsininventory.EZ-Windows'managementteamwouldliketode-velop a production schedule for the next three moths.A smooth production scheduleis obviously desirable because it maintains the current workforce and provides a sim-ilar month-to-month operation. However, given the sales forecasts, the productioncapacities, and the storage capabilities as shown in Table 2, the management teamdoes not think a smooth production schedule with the same production quantity eachmonthpossible.

The company's cost accounting department estimates that increasing productionbyonewindowfromonemonthtothenextwillincreasetotalcostsby$1.00foreach

Table2:Problem1.8

	February	March	April
Salesforecast	15,000	16,500	20,000
Productioncapacity	14,000	14,000	18,000
Storagecapacity	6,000	6,000	6,000

unit increase in the production level. In addition, decreasing production by one unitfrom one month to the next will increase total costs by $0.65 for each unit decrease inthe production level.Ignoring production and inventory carrying costs, formulate alinear programming model that will minimize the cost of changing production levelswhilestillsatisfyingthemonthlysalesforecasts.