A lumber company operates a sawmill that converts timber to lumber or plywood. A marketable mix of 1000 board feet of lumber products requires 1000 board feet of spruce and 4000 board feet of Douglas r. Producing 1000 square feet of plywood requires 2000 board feet of spruce and 4000 board feet of r. The company's timberland yields 32,000 board feet of spruce and 72,000 board feet of r each season.

Sales commitments require that at least 5000 board feet of lumber and 12,000 board feet of plywood be produced during the season. The prot contributions are $45 per 1000 board feet of lumber and $60 per 1000 square feet of plywood.

a) Express the problem as a linear programming model.

b) Graph the problem and indicate the optimal solution on the graph.