ClearVu Glass Co. Produces high-quality glass products, including window and glass doors. Although the products are expensive, they fill a market niche by providing the highest quality available in the industry for the most discriminating buyer. The company has three plants that simultaneously produce the components of its products. Plant 1 produces aluminum frames and hardware, Plant 2 produces wood frames, and Plant 3 produces the glass and assembles the windows and doors. Top management has decided to revamp the company's product line by discontinuing unprofitable models which has released production capacity to launch two new products: an 8-foot glass door and a 4 by 6-foot double-hung window. ClearVu management needs determine how many units to produce of each of the new products per week. The table below shows the resources used by each product and available at each plant each week.
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Production time used for each unit
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Time available per week
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Doors
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Windows
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|
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Plant 1
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1 hour
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0 hours
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4 hours
|
|
Plant 2
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0 hours
|
2 hours
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12 hours
|
|
Plant 3
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3 hours
|
2 hours
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18 hours
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Each door produced will contribute $300 to ClearVu's profit, while each window produced contributes $500.
Write the linear programming formulation to help ClearVu management determine how many units of each product they should produce per week.