Blue Ridge Hot Tubs Company
       • Howie Jones owns and operates Blue Ridge Hot Tubs, a company that sells two models of hot 
        tubs: the Aqua-Spa and the Hydro-Lux. 
       • Howie purchases prefabricated fiberglass hot tub shells and installs a common water pump and 
        the appropriate amount of tubing into each hot tub. 
       • Every Aqua-Spa requires 9 hours of labor and 12 feet of tubing; every Hydro-Lux requires 6 hours 
        of labor and 16 feet of tubing. 
       • Demand for these products is such that each Aqua-Spa produced can be sold to generate a profit 
        of $350, and each Hydro-Lux produced can be sold to generate a profit of $300. 
       • The company expects to have 200 pumps, 1,566 hours of labor, and 2,880 feet of tubing available 
        during the next production cycle. 
       • The problem is to determine the optimal number of Aqua-Spas and Hydro-Luxes to produce to 
        maximize profits.                                                 2
         Blue Ridge Hot Tubs Company
         • Decision variables:
         •  
            : number of Aqua-Spas to produce
            : number of Hydro-Luxes to produce
         • Objective function (profit):
         • Constraints:
            Pump: 
            Labor: 
            Tubing: 
            Non-negativity: 
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       Blue Ridge Hot Tubs Company Mathematical Model
       •  
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           Blue Ridge Hot Tubs Company Spreadsheet Modeling
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       Sensitivity Analysis
       • Sensitivity analysis helps answer questions about how sensitive the optimal solution is to 
        changes in various coefficients in an LP model.
       Approaches to Sensitivity Analysis:
       • Change the data and re-solve the model!
          • Sometimes this is the only practical approach.
       • Solver also produces sensitivity reports that can answer questions about:
          • amounts objective function coefficients can change without changing the solution.
          • the impact on the optimal objective function value of changes in various constrained 
           resources.
          • the impact on the optimal objective function value of forced changes in certain decision 
           variables.
          • the impact changes in constraint coefficients will have on the optimal solution.
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