The Tim Burr Company wants to best utilize the wood resources in one of its forest regions. Within this region, there is a saw mill and a plywood mill; thus, timber can be converted to lumber or plywood.

Producing a marketable mix of 1000 board feet of lumber products requires 1000 board feet of spruce and 3000 board feet of Douglas fir. Producing 1000 square feet of plywood requires 2000 board feet of spruce and 4000 board feet of Douglas fir. This region has available 32,000 board feet of spruce and 72,000 board feet of Douglas fir. 

Sales commitments require that at least 4000 board feet of lumber and 12,000 square feet of plywood be produced during the planning period. The profit contributions are $40 per 1000 board feet of lumber products and $60 per 1000 square feet of plywood. The company is interested in maximizing profits. Provide a linear programming model formulation and solve for an optimal solution.