Bangs Leisure Chairs produces three types of hand-crafted outdoor chairs that are popular for beach, pool and patios: sling chair, Adirondack chairs, and hammocks. The unit profit for these products is $35, $75, and $100, respectively. Each type of chair requires cutting, assembling, and finishing. The owner is retired and is willing to work 6 hours/day for 5 days/week, so has 120 hours available each month. He does not want to spend more than 50 hours each month on any one activity (i.e., cutting, assembling, and finishing). The retailer he works with is certain that all products he makes can easily be sold.
Sling chairs are made of 10 wood pieces for the frame, and one piece of cloth. The actual cutting of the wood takes 30 minutes. Assembling includes sewing of the fabric and the attachment of rivets, screws, fabric, and dowel rod and takes 45 minutes. The finishing stage involves sanding, staining, and varnishing of the various parts and takes 1 hour. Adirondack chairs take 2 hours for both the cutting and assembling phases, and finishing takes 1 hour. For hammocks, cutting takes 0.4 hours, assembly takes 3 hours, and finishing also takes 1 hour. How many of each type of chair should be produce each month to maximize profit?
Develop and solve a linear optimization model. (Since the business is ongoing, fractional solutions are acceptable!)
Suppose Mr. Bangs wants to limit the number of sling chairs to at most 25. How then, will the solution be?
Suppose that Mr. Bang changes his mind of limiting the sling chair production, but instead, does not want to spend more than 40 hours each month on any one activity. How will the solution change from part a)?