Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux. Howie Jones, the owner and manager of the company, needs to decide how many of each type of hot tub to produce during his next production cycle. Howie buys prefabricated fiberglass hot tub shells from a local supplier and adds the pump and tubing to the shells to create his hot tubs. (This supplier has the capacity to deliver as many hot tub shells as Howie needs). Howie 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 labor required. Each Aqua-Spa requires 9 hours of labor and 12 feet of tubing. Each HydroLux requires 6 hours of labor and 16 feet of tubing. Howie expects to have 1,566 production labor hours and 2,880 feet of tubing available during next production cycle. Howie earns a profit of $350 on each Aqua-Spa he sells and $300 on each Hydro-Lux he sells. He is confident that he can sell all the hot tubs he produces. The questions is, how many Aqua-Spas and HydroLuxes should Howie produce if he wants to maximize his profit during the next production cycle?

DVs (USALT):

Objective function:

Constraints:

Non-negativity constraints:

Solve by first formulating the problem using A and H as decision variables for number of Aqua-Spas and Hydro-Lux models respectively (write the objective function and constraints, ignore USALT for now). After formulating the problem, solve it graphically and then with Excel.

Please solve in Excel and show graphical solution and model.