Question: The Outdoor Furniture Corporation manufactures three products, benches, picnic tables, and chairs. The firm has three main resources: carpenters, painters, and a supply of lumber. Each month 1,800 hours of carpentry time are available, 1,200 hours of painting time are available, and 4,800 feet of wood are available. Each bench requires 3 hours of carpentry time, 2 hours of painting time, and 10 feet of wood. Each picnic table requires 6 hours of carpentry time, 5 hours of painting time, and 35 feet of wood. Each chair requires 5 hours of carpentry time, 4 hours of painting time, and 12 feet of wood. The profit for benches, tables, and chairs are $30, 50, and 40 respectively. The company would like to maximize profit given the resources available and linear programming is to be used for this purpose.

a) Carefully define the decision variables.

b) Formulate the linear program.

c) Solve the linear program and fill in the information below.