Three of Weigelt's plants have spare capacity, and the company is preparing to produce a new product. Fortunately, all three plants can produce this product, so the spare capacity can be used. The product is divided into three models, large, medium and small, and its unit net income is $420, $360 and $300, respectively. Factory 1, Factory 2, Factory 3 have a production capacity of 750, 900 and 450 products per day, respectively (regardless of the model or combination of models). The available storage space in the production process is also a factor limiting the production of new products, Factory 1, Factory 2, Factory 3 can provide 13,000, 12,000 and 5,000 square feet of process storage space per day for this product, per 1 unit of large, medium, Small products require 20, 15, and 12 square feet of storage space, respectively. Sales forecasts estimate that 900, 1,200 and 750 large, medium and small products can be sold per day, respectively. Management wants to know the number of different models that each factory should make in order to maximize profits. 

Build a linear programming model for this problem on a spreadsheet and solve it.

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