Question: Dolly Trolleys manufacture trolleys for a chain of supermarkets. Demand for trolleys is buoyant, so all production can be sold. Two models are produced by Dolly - the STREAMLINE (L) and the STANDARD (D). The streamline has three wheels and the standard has four. The daily availability of wheels (which are bought in) is limited to 240. Dolly works a single 8-hour shift per day. There are two stages of manufacture for trolleys: fabrication and spraying. Spraying takes 24 minutes for each streamline trolley and 10 minutes for each standard. Fabrication takes 30 minutes for each streamline trolley and 20 minutes for each standard. Three identical machines are available for fabrication, which can be used for either type of trolley (or both).

Spraying is carried out manually by one person per trolley, and there are two staff available for this process. The profit from selling a streamline trolley is $20 and a standard trolley is $18. No more than 15 trolleys can be produced per hour because of storage limitations on work in progress. Develop a linear programming model for this problem. Use a graphical technique to determine the optimal solution for the Dolly Trolleys manufacturing company, including exact values for the variables (solving simultaneous equations where necessary).