Question

Blue Ridge Hot Tubs 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 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?

1- For each statement below, determine whether the statement is a decision variable or not.
* Number of Aqua-Spa Produced.
* Number of Hydro-Lux Produced.
* Number of Pumps Purchased.
* Amount of Available Labor Hours.
* Amount of Available Tubing Available.
* Profit of Aqua-Spa.
* Profit of Hydro-Lux.

Answer 1

Ans.: Profit $350 $300 Availability Hydro-Lux Aqua-Spa, x Pumps 200 Tubin 12 16 2880 Labor 1566

240 12x+16y 2880 A(0,180) x+y= 200 A(0, 180) 12x+16y 28(80,120) 160 B(80, 120) 120 x + y = 200 9+6y 156C(22,78) 9x+6y = 1566), D (174, 0) C(122,78) 80 40 Jx -400 360 320 280 240 200 -160 -120 -80 40 40 80 120 160 24 D(174, 0) -40 350x + 300y z -80 A(0,180)z 350x0+300x180 $54,000 4(80,120)→ z=350x 80+300 x 120=$64,000 A (0, 180) z = 350x 122 + 300x78 = $66, 100 4(174,0) → z 350x 174 + 300x0-$60.900 Maximize z 350x+ 300y Subject to 120 rty200 Maamm 160 12x+16y S2880 9x+6y S1566 200 x20,y20