Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux. Mr. John Bediako, the owner and manager of the company, needs to decide how many of each type of hot tub to produce during his next production cyle. John buys prefabricated fiberglass hot tub shells from a local suppler and adds the pump and tubing to the shells to create his hot tubs. John installs the same type of pump into both hot tubs. He will have only 200 pumps available during his next production cycle. From a manufacturing standpoint, the main difference between the two models of hot tubs is the amount of tubing and labour required. Each Aqua-Spa requires 9 hours of labour and 12 feet of tubing. Each Hydro-Lux requires 6 hours of labour and 16 feet of tubing. John expects to have 1566 production labour hours and 2880 feet of tubing available during the next production cycle. John earns a profit of GH¢350 on each Aqua-Spa he sells and GH¢300 on each Hydro-Lux he sells. He is confident that he can sell all the hot tubs that he produces. Define the decision variables for John’s production problem. Formulate a linear programming model for this problem. Solve this model by using graphical analysis.
Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux. Mr. John Bediako, the owner and manager of the company, needs to decide how many of each type of hot tub to produce during his next production cyle. John buys prefabricated fiberglass hot tub shells from a local suppler and adds the pump and tubing to the shells to create his hot tubs. John installs the same type of pump into both hot tubs. He will have only 200 pumps available during his next production cycle. From a manufacturing standpoint, the main difference between the two models of hot tubs is the amount of tubing and labour required. Each Aqua-Spa requires 9 hours of labour and 12 feet of tubing. Each Hydro-Lux requires 6 hours of labour and 16 feet of tubing. John expects to have 1566 production labour hours and 2880 feet of tubing available during the next production cycle. John earns a profit of GH¢350 on each Aqua-Spa he sells and GH¢300 on each Hydro-Lux he sells. He is confident that he can sell all the hot tubs that he produces.
- Define the decision variables for John’s production problem.
- Formulate a linear programming model for this problem.
- Solve this model by using graphical analysis.
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