Question

Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the HydroLux. 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 can deliver as many hot tub shells as Howie needs.) Howie installs the same type of pump for 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 Hydro-Lux 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 the 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 question is, how many Aqua-Spas and Hydro-Luxes should Howie produce if he wants to maximize his profits during the next production cycle

Answer 1

Answer:

Using Excel solver, the optimal solution is: 122 Aqua-Spa + 78 Hydro-Lux, and the maximum profit = $66,100

Explanation:

you have to maximize the following equation: 350A + 300H

where:

A = number of Aqua-Spa hot tubs sold

H = number of Hydro-Lux hot tubs sold

the constraints are:

A + H ≤ 200     ⇒ number of water pumps available

9A + 6H ≤ 1,566      ⇒ number of labor hours available

12A + 16H ≤ 2,880      ⇒ number of feet of tubing available

A ≥ 0      ⇒ non-negative numbers

B ≥ 0      ⇒ non-negative numbers

both A and B are integers    

Using Excel solver, the optimal solution is: 122A + 78B, and the maximum profit = $66,100