Problem
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 common water pumps and the appropriate amount of tubing into each hot tub. Every Aqua-Spa requires a pump, 12 hours of labor and 16 feet of tubing; every Hydro-Lux requires 2 pumps, 16 hours of labor and 8 feet of tubing. Demand for these products is such that each Aqua-Spa produced can be sold to generate a profit of $275, and each Hydro-Lux produced can be sold to generate a profit of $250. The company expects to have 450 pumps, 91 workers, and 3,080 feet of tubing available during the next week's production cycle. Determine the optimal number of Aqua-Spas and Hydro-Luxes to produce to maximize profit assuming all employees work their 40 hours with no overtime.
1) What are the objective function, decision variables, and constraints for this optimization problem?
2) Develop an Excel spreadsheet and use Excel-Solver to find an optimal solution for this problem.
3) Describe the optimal solution in words.